En la teoría de números recreativos , un número primo único o un número primo único es un cierto tipo de número primo . Un primo p ≠ 2, 5 se llama único si no hay otro primo q tal que la longitud del período de la expansión decimal de su recíproco , 1 / p , sea igual a la longitud del período del recíproco de q , 1 / q . [1]Por ejemplo, 3 es el único primo con el período 1, 11 es el único primo con el período 2, 37 es el único primo con el período 3, 101 es el único primo con el período 4, por lo que son primos únicos. Por el contrario, 41 y 271 tienen el período 5; 7 y 13 tienen ambos el período 6; 239 y 4649 ambos tienen el período 7; 73 y 137 ambos tienen período 8; 21649 y 513239 ambos tienen período 11; 53, 79 y 265371653 tienen todos el período 13; 31 y 2906161 ambos tienen período 15; 17 y 5882353 ambos tienen el período 16; 2071723 y 5363222357 ambos tienen el período 17; 19 y 52579 tienen el período 18; 3541 y 27961 tienen el período 20. Por lo tanto, ninguno de estos es un número primo único. Los números primos únicos fueron descritos por primera vez por Samuel Yates en 1980.
No. de términos conocidos | 102 |
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Conjeturaba que no. de términos | Infinito |
Primeros términos | 3 , 11 , 37 , 101 |
Término más grande conocido | (10 270343 -1) / 9 |
Índice OEIS |
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La definición anterior está relacionada con la representación decimal de números enteros . Se pueden definir números primos únicos y se han estudiado en cualquier base numérica .
Periodo de prima en base b
La representación del recíproco de un número primo (o, más generalmente, un entero ) p en la base numérica b es periódica del período n si
donde q es un número entero positivo menor queDe acuerdo con la fórmula de suma de series geométricas , esto puede reescribirse como
En otras palabras, n es un período de la representación de 1 / p si y solo si p es un divisor de El teorema de Euler afirma que, si un entero b es coprimo con p , entonces p es un divisor de dónde es la función totient de Euler . Esto prueba que, para cada entero p coprime con b , la representación del recíproco de p es periódica en base b .
Todos los períodos de una función periódica son múltiplos de un período más corto generalmente llamado período fundamental. En este artículo, llamamos período de p en base b al período más corto de la representación de 1 / p en base b . Por lo tanto, el período de p en base b es el menor entero positivo n tal que p es un divisor deEn otras palabras, el período de un primo p en base b es el orden multiplicativo de b módulo p .
Según el teorema de Zsigmondy , todo entero positivo es un período de algún primo en base b excepto en los siguientes casos:
- b = 2 y n = 1 o 6
- n = 2 y b = 2 k - 1 para algún entero k > 1
Como
dónde es el n - ésimo polinomio ciclotómico , los números primos del período n en la base b son divisores primos deMás precisamente, los números primos del período n son exactamente los divisores primos deque no dividen n (ver más abajo para una prueba de este resultado y de los siguientes).
Si b es par (esto incluye los casos binario y decimal), los divisores primos deque no dividen n son exactamente los divisores primos de [ cita requerida ]
Esto es incorrecto si b es impar: si n = 2 y b = 4 k - 1 , donde k es un número entero positivo, entonces
aunque 2 divide a n = 2 y
Si b es impar, los números primos del período n son exactamente, si n = 1 , los divisores primos de, o, si n > 1 , los divisores primos impares de R n ( b ) .
Croquis de la prueba de caracterización de primos del período n |
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Como el período de todo primo p divide p - 1 ( el pequeño teorema de Fermat ), si p divide n , entonces su período es menor que n . Por el contrario, si p dividey tiene un período k menor que n , entonces es un divisor común de y Como la resultante de dos polinomios es una combinación lineal de estos polinomios, p divide la resultante de y Como estos dos polinomios son coprime y dividen p divide también al discriminante de Por tanto, un divisor primo de , que tiene un período menor que n , también es divisor de n . Ahora, tenemos que demostrar que, si un número primo p > 2 divisiones n y entonces no divide De hecho, esto implica inmediatamente que p no divideSi b es par, 2 no puede dividir(que es impar), y la condición p > 2 no es restrictiva. Por tanto, sea n = pm . Basta probar queno divide S ( b ) para algún polinomio S ( x ) , que es un múltiplo de Nosotros tomamos Según el pequeño teorema de Fermat , tenemosComo p divide, también tenemos Así, el orden multiplicativo de b módulo p divide a mcd ( n , p - 1) , que es un divisor de m = n / p . Por tanto, c = b m - 1 es un múltiplo de p . Ahora, Como p es primo y mayor que 2, todos los términos excepto el primero son múltiplos de Esto prueba que no divide |
Un primo p es un primo único en base b , si y solo si, para algún n , es el divisor primo único deque no divide n . Si b es par (que incluye los casos binario y decimal) esto significa que
para algún entero positivo c .
Si b es impar, esto significa que
para algunos enteros c > 0 y d ≥ 0 . Esto proporciona un método eficaz para calcular los números primos únicos y los números primos de un período determinado.
Tenga en cuenta que un divisor primo de b es coprime con, y así también con su divisor Tal número primo no tiene duración de período, ya que la representación en base b de su recíproco es finita en lugar de periódica. Por lo tanto, tal primo nunca se considera un primo único, incluso si es el primo único que tiene un recíproco finito en la base b . Por ejemplo, 2 no se considera como primo único en binario, aunque es el único primo con recíproco finito en binario.
Hay cuatro situaciones de prima única en base b :
- y p es primo.
- y p es primo y.
- y p es primo y.
- y p es primo y y .
Conjeturas:
- Para todos los enteros positivos n , hay un número infinito de bases b tales que hay un número primo único con una longitud de período n . (esta conjetura es cierta si la conjetura de Bunyakowsky es verdadera, ya que los polinomios ciclotómicos son irreducibles)
- Para todas las bases b , hay infinitos números primos únicos.
- Para todos los enteros positivos n , hay un número infinito de bases b, de modo que hay un número primo único con una longitud de período n, que es la primera situación. (es decir, para todo n ≥1, hay infinitos b ≥2 tales que es primo, donde es el polinomio ciclotómico ) (esta conjetura es verdadera si la conjetura de Bunyakowsky es cierta, ya que los polinomios ciclotómicos son irreducibles)
- Para todas las bases b , hay infinitos números primos únicos que son la primera situación. (es decir, para todo b ≥2, hay infinitos n ≥1 tales que es primo, donde es el polinomio ciclotómico )
- Para todos los enteros positivos n que no están en (secuencia A253235 en el OEIS ), hay infinitas bases b, de modo que hay un número primo único con una longitud de período n, que es la segunda situación. (las longitudes de los períodos n en (secuencia A253235 en el OEIS ) no pueden tener ninguna base, que es la segunda o la cuarta situación) (esta conjetura es cierta si la conjetura de Bunyakowsky es cierta, ya que los polinomios ciclotómicos son irreducibles)
- Para todas las bases b , solo hay un número finito de números primos únicos (o no hay primos únicos) que son la segunda situación, especialmente, en la base 2, los únicos períodos conocidos que son la segunda situación son 18, 20, 21, 54, 147, 342, 602, 889, 258121, y en base 10, los únicos períodos conocidos que son la segunda situación son 3, 9, 294.
- Todos los combos (período n , base b ) que es la tercera situación son
- n = 1, b = p c +1 con p primo y c ≥ 2
- n = 2, b = p c −1 con p primos impares y c ≥ 2
- n = 3, b = 18
- n = 5, b = 3
- n = 6, b = 19
- Todos los combos (período n , base b ) que es la cuarta situación son
- n = 2, b = 2 r p c −1 con p primos impares y r ≥ 1 y c ≥ 2
- n = 3, b en (secuencia A028231 en la OEIS ) en el caso de ( b 2 + b +1) / 3 es cuadrado de primos (se conjetura que potencias con exponente> 2 no pueden existir) (la primera de tales bases b son 22, 313, 4366, 847078, ...) (los primos correspondientes están en (secuencia A001570 en la OEIS ))
- n = 4, b en (secuencia A002315 en la OEIS ) en el caso de ( b 2 +1) / 2 es cuadrado de primo o 28561 = 13 4 (se conjetura que potencias con exponente> 2 no pueden existir, excepto (239 2 +1) / 2 = 28561 = 13 4 ) (las primeras bases b son 7, 41, 239, 8119, 47321, ...) (los primos correspondientes están en (secuencia A001563 en la OEIS ))
- n = 6, b −1 en (secuencia A028231 en el OEIS ) en el caso de ( b 2 - b +1) / 3 es cuadrado de primos (se conjetura que las potencias con exponente> 2 no pueden existir) (la primera las bases b son 23, 314, 4367, 847079, ...) (los primos correspondientes están en (secuencia A001570 en la OEIS ))
- Especialmente, no existe ningún combo (período n , base b ) que sea la tercera o cuarta situación para n > 6
- "Casi todos" (período n , base b ) los combos son la primera situación
(Para todos los combo (período n , base b ) que es la tercera o cuarta situación, el primo p correspondiente debe generalizarse como primo de Wieferich a la base b )
Tabla de los periodos de primos hasta 139 en bases hasta 24 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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La mención "terminado" significa que el primo divide la base y, por lo tanto, la representación de su recíproco es finita.
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Tabla de primos de un período determinado (hasta 24) en bases hasta 24 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Negrita para primos únicos.
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Primos únicos decimales
En la actualidad, se conocen más de cincuenta números primos únicos o probables . Sin embargo, solo hay veintitrés números primos únicos por debajo de 10 100 . La siguiente tabla enumera los 23 primos únicas por debajo de 10 100 (secuencia A040017 (ordenados) y A007615 (clasificadas por longitud de periodo) en OEIS ) y sus periodos (secuencia A051627 (clasificadas por números primos correspondiente) y A007498 (ordenada) en OEIS )
principal | |
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1 | 3 |
2 | 11 |
3 | 37 |
4 | 101 |
10 | 9.091 |
12 | 9,901 |
9 | 333.667 |
14 | 909,091 |
24 | 99,990,001 |
36 | 999,999,000,001 |
48 | 9,999,999,900,000,001 |
38 | 909,090,909,090,909,091 |
19 | 1,111,111,111,111,111,111 |
23 | 11,111,111,111,111,111,111,111 |
39 | 900,900,900,900,990,990,990,991 |
62 | 909,090,909,090,909,090,909,090,909,091 |
120 | 100,009,999,999,899,989,999,000,000,010,001 |
150 | 10,000,099,999,999,989,999,899,999,000,000,000,100,001 |
106 | 9.090.909.090.909.090.909.090.909.090.909.090.909.090.909.090.909.091 |
93 | 900,900,900,900,900,900,900,900,900,900,990,990,990,990,990,990,990,990,990,991 |
134 | 909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,091 |
294 | 142,857,157,142,857,142,856,999,999,985,714,285,714,285,857,142,857,142,855,714,285,571,428,571,428,572,857,143 |
196 | 999,999,999,999,990,000,000,000,000,099,999,999,999,999,000,000,000,000,009,999,999,999,999,900,000,000,000,001 |
El número primo con una duración de período 294 es similar [ aclaración necesaria ] al recíproco de 7 (0.142857142857142857 ...)
Justo después de la tabla, el vigésimo cuarto número primo único tiene 128 dígitos y una longitud de período de 320. Se puede escribir como (9 32 0 32 ) 2 + 1, donde un número de subíndice n indica n copias consecutivas del dígito o grupo de dígitos. antes del subíndice.
Aunque son raros, basados en la ocurrencia de primos de repunit y primes probables, se conjetura fuertemente que hay infinitos primos únicos. (Cualquier prima de repunit es única).
A partir de 2010[actualizar]el repunit (10 270343 - 1) / 9 es el número primo único probable más grande conocido. [2]
En 1996, el número primo único probado más grande era (10 1132 + 1) / 10001 o, usando la notación anterior, (99990000) 141 + 1. Tiene 1128 dígitos. El récord se ha mejorado muchas veces desde entonces. A partir de 2020[actualizar] la prima única probada más grande es , tiene 20160 dígitos. [3]
Primos únicos binarios
Los primeros primos únicos en binario (base 2) son:
- 3, 5, 7, 11, 13, 17, 19, 31, 41, 43, 73, 127, 151, 241, 257, 331, 337, 683, ... (secuencia A144755 (ordenada) y A161509 (ordenada por duración del período) en OEIS )
La duración del período de ellos es:
- 2, 4, 3, 10, 12, 8, 18, 5, 20, 14, 9, 7, 15, 24, 16, 30, 21, 22, ... (secuencia A247071 (ordenada por los números primos correspondientes) y A161508 (ordenado) en OEIS)
Incluyen números primos de Fermat (la duración del período es una potencia de 2 ), números primos de Mersenne (la duración del período es un número primo ) y números primos de Wagstaff (la duración del período es el doble de un número primo impar ).
Además, si n es un número natural que no es igual a 1 o 6, entonces al menos un número primo tiene un período n en base 2, debido al teorema de Zsigmondy . Además, si n es congruente con 4 (mod 8) y n > 20, entonces al menos dos primos tienen un período n en base 2 (por lo tanto, n no es un período único en base 2) debido a la factorización de Aurifeuillean , por ejemplo , 113 () y 29 () ambos tienen período 28 en base 2, 37 () y 109 () ambos tienen período 36 en base 2, y que 397 () y 2113 () ambos tienen período 44 en base 2,
Como se muestra arriba, un primo p es un primo único del período n en base 2 si y solo si existe un número natural c tal que
Empíricamente, parece que la mayoría de los casos corresponden al denominador siendo 1, entonces tenemos un primo (o poder primo) de forma . Sin embargo, para n igual a 18, 20, 21, 54, 147, ... (secuencia A333973 en el OEIS ), obtenemos un número primo binario único aunquetiene un pequeño divisor (que se comparte con n ).
De hecho, no hay primo con c > 1 (es decires un verdadero poder de p ), y todos los primos únicos conocidos p tienen c = 1. Se conjetura que todos los primos únicos tienen c = 1 (es decir, todos los primos únicos en base 2 no son primos de Wieferich ).
A partir de septiembre de 2019, el número primo único de base 2 más grande conocido es 2 82589933 -1, también es el número primo principal más grande conocido. Con la excepción de los primos de Mersenne, el primo único probable de base 2 más grande conocido es, [4] y la prima única de base 2 probada más grande es. Además, la prima única probable de base 2 más grande conocida que no es la prima de Mersenne ni la prima de Wagstaff es.
Similar a la base 10, aunque son raros (pero más que en el caso de la base 10), se conjetura que hay infinitos números primos únicos en base 2, porque todos los primos de Mersenne son únicos en base 2, y se conjetura que existen. infinitos números primos de Mersenne. [ cita requerida ]
No dividen ninguno de los pseudoprimos hasta la base 2, pero cada otro número primo impar divide un pseudoprime hasta la base 2, porque si y solo si un número compuesto se puede escribir como, es un overpseudoprime a la base 2. [ aclaración necesaria ]
Hay 52 números primos únicos en base 2 por debajo de 2 64 , son:
Prime (escrito en decimal) | Prime (escrito en binario) | |
---|---|---|
2 | 3 | 11 |
4 | 5 | 101 |
3 | 7 | 111 |
10 | 11 | 1011 |
12 | 13 | 1101 |
8 | 17 | 1 0001 |
18 | 19 | 1 0011 |
5 | 31 | 1 1111 |
20 | 41 | 10 1001 |
14 | 43 | 10 1011 |
9 | 73 | 100 1001 |
7 | 127 | 111 1111 |
15 | 151 | 1001 0111 |
24 | 241 | 1111 0001 |
dieciséis | 257 | 1 0000 0001 |
30 | 331 | 1 0100 1011 |
21 | 337 | 1 0101 0001 |
22 | 683 | 10 1010 1011 |
26 | 2,731 | 1010 1010 1011 |
42 | 5.419 | 1 0101 0010 1011 |
13 | 8.191 | 1 1111 1111 1111 |
34 | 43,691 | 1010 1010 1010 1011 |
40 | 61.681 | 1111 0000 1111 0001 |
32 | 65.537 | 1 0000 0000 0000 0001 |
54 | 87,211 | 1 0101 0100 1010 1011 |
17 | 131,071 | 1 1111 1111 1111 1111 |
38 | 174,763 | 10 1010 1010 1010 1011 |
27 | 262,657 | 100 0000 0010 0000 0001 |
19 | 524,287 | 111 1111 1111 1111 1111 |
33 | 599,479 | 1001 0010 0101 1011 0111 |
46 | 2,796,203 | 10 1010 1010 1010 1010 1011 |
56 | 15,790,321 | 1111 0000 1111 0000 1111 0001 |
90 | 18,837,001 | 1 0001 1111 0110 1110 0000 1001 |
78 | 22,366,891 | 1 0101 0101 0100 1010 1010 1011 |
62 | 715,827,883 | 10 1010 1010 1010 1010 1010 1010 1011 |
31 | 2,147,483,647 | 111 1111 1111 1111 1111 1111 1111 1111 |
80 | 4.278.255.361 | 1111 1111 0000 0000 1111 1111 0000 0001 |
120 | 4,562,284,561 | 1 0000 1111 1110 1110 1111 0000 0001 0001 |
126 | 77,158,673,929 | 1 0001 1111 0111 0000 0011 1110 1110 0000 1001 |
150 | 1,133,836,730,401 | 1 0000 0111 1111 1101 1110 1111 1000 0000 0010 0001 |
86 | 2,932,031,007,403 | 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 1011 |
98 | 4.363.953.127.297 | 11 1111 1000 0000 1111 1110 0000 0011 1111 1000 0001 |
49 | 4.432.676.798.593 | 100 0000 1000 0001 0000 0010 0000 0100 0000 1000 0001 |
69 | 10.052.678.938.039 | 1001 0010 0100 1001 0010 0101 1011 0110 1101 1011 0111 |
sesenta y cinco | 145,295,143,558,111 | 1000 0100 0010 0101 0010 1001 0110 1011 0101 1011 1101 1111 |
174 | 96,076,791,871,613,611 | 1 0101 0101 0101 0101 0101 0101 0100 1010 1010 1010 1010 1010 1010 1011 |
77 | 581,283,643,249,112,959 | 1000 0001 0001 0010 0010 0110 0100 1100 1101 1001 1011 1011 0111 0111 1111 |
93 | 658,812,288,653,553,079 | 1001 0010 0100 1001 0010 0100 1001 0011 0110 1101 1011 0110 1101 1011 0111 |
122 | 768,614,336,404,564,651 | 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1011 |
61 | 2.305.843.009.213.693.951 | 1 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 |
85 | 9.520.972.806.333.758.431 | 1000 0100 0010 0001 0100 1010 0101 0010 1011 0101 1010 1101 0111 1011 1101 1111 |
192 | 18,446,744,069,414,584,321 | 1111 1111 1111 1111 1111 1111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0001 |
Después de la tabla, los siguientes 10 primos binarios únicos tienen una longitud de período de 170, 234, 158, 165, 147, 129, 184, 89, 208 y 312. Además, los bits (dígitos en binario) de ellos son 65, 73, 78, 81, 82, 84, 88, 89, 96 y 97.
Primos bi-únicos
Los números primos bi-únicos son pares de números primos que comparten una duración de período entre sí, pero sin otros números primos. Por ejemplo, en binario, los primos bi-únicos con al menos un primo menor que 10000 son:
primer p | el único otro primo que tiene el mismo período que p | duración del período |
---|---|---|
23 | 89 | 11 |
29 | 113 | 28 |
37 | 109 | 36 |
47 | 178481 | 23 |
59 | 3033169 | 58 |
61 | 1321 | 60 |
67 | 20857 | 66 |
71 | 122921 | 35 |
79 | 121369 | 39 |
83 | 8831418697 | 82 |
89 | 23 | 11 |
97 | 673 | 48 |
107 | 28059810762433 | 106 |
109 | 37 | 36 |
113 | 29 | 28 |
139 | 168749965921 | 138 |
167 | 57912614113275649087721 | 83 |
193 | 22253377 | 96 |
223 | 616318177 | 37 |
251 | 4051 | 50 |
263 | 10350794431055162386718619237468234569 | 131 |
281 | 86171 | 70 |
283 | 165768537521 | 94 |
353 | 2931542417 | 88 |
397 | 2113 | 44 |
433 | 38737 | 72 |
463 | 4982397651178256151338302204762057 | 231 |
571 | 160465489 | 114 |
577 | 487824887233 | 144 |
601 | 1801 | 25 |
607 | 1512768222413735255864403005264105839324374778520631853993 | 303 |
631 | 23311 | 45 |
641 | 6700417 | 64 |
643 | 84115747449047881488635567801 | 214 |
673 | 97 | 48 |
727 | 1786393878363164227858270210279 | 121 |
751 | 2139731020464054092520609592459940706818275139793055476751 | 375 |
769 | 442499826945303593556473164314770689 | 384 |
919 | 75582488424179347083438319 | 153 |
1039 | 19709014643115560219397264671577125505264032974428376489237001990435774189483906244488746953221813209 | 519 |
1291 | 83861817871925183739792206470703862766563053456867813459969184678546547694793573468589875745315081 | 1290 |
1321 | 61 | 60 |
1327 | 2365454398418399772605086209214363458552839866247069233 | 221 |
1429 | 14449 | 84 |
1471 | 252359902034571016856214298851708529738525821631 | 245 |
1543 | 4965395030068548134274243124972075225434447114375481299036593442726326832727934403424309955102162841656341524725641213163998408700663382552888660520657 | 771 |
1697 | 99335205800663868215396640964567095667094665346141013294320587365443384719802857319737050495099341955640963272958071602273 | 848 |
1753 | 1795918038741070627 | 146 |
1777 | 25781083 | 74 |
1801 | 601 | 25 |
2113 | 397 | 44 |
2281 | 3011347479614249131 | 190 |
2801 | 1114513219367157067542813609361306957257890531134775327875067038594481393220804051366788787128409731513666376851495151281817670381468528387601 | 1400 |
2971 | 48912491 | 110 |
3011 | 631215008947706187342830494125660733360092019659681922883823392015121754384870744044074337887482936870852519582960673945561810148710850934449712549090934572292098088972061029650939105592263256293676274598529593937386833315889748213948490958132757432166701901197169972066727635929332437543971934775961 | 3010 |
3259 | 960843850986532976532466235773483492840618819232206145010143480044702708779967241439519037158800917230289 | 1086 |
3361 | 88959882481 | 168 |
3967 | 3296810823331827444014404831943558588631803435050404237042485765714486337505843011741487225539321479275976317423474114853376321380782906502106758766783934866952124117240484839332668914566806988602931402117416523955329423560856334826333176954575294550104263404414368761262079586842542586869780254842277261781328657636993064897732127711363870426953852536828242291991249685206783121190349820804553 | 1983 |
4051 | 251 | 50 |
4129 | 33770734168253651800370989375796994825389296318018601048482005531172856260013942500368975908606689 | 688 |
4177 | 9857737155463 | 87 |
4523 | 106788290443848295284382097033 | 266 |
4561 | 51049903050598156013062477654241640657829025002976204451060261008689478158715729745160924860467530309657376827104233308157772350164622158651187694109112727796663977157921 | 2280 |
4871 | 82033219963138371097689272308258116841679442057301643873942124991182012434598644913857356023840478815121709542915222280972560231358838127531337 | 487 |
5153 | 54410972897 | 112 |
5281 | 86057341436900896945763810153382736470468416428618882438399687147162676446821942943285064979823448879103697729595218530528136858692236024016183057049788583024181216322 | 2640 |
5347 | 242099935645987 | 198 |
5431 | 9496792988973395279834809661569251320544014305629535339041176003993804676485199470146061766714674245857484692035146769896735263094609746643655454990307740324793870789211183639302657602006206727998357155351588374904926882678074633252877772442134938712719216422825919305415646969838444956229559805502059906228691551284152908049964563516405524127028294884716508273187514617905113012642316992618568629664046915514871575875088457784721 | 2715 |
5881 | 23618256244840618857212522155851714598259422753496906641681177748710460515038403366198473773770441 | 1470 |
6043 | 4475130366518102084427698737 | 318 |
6659 | 67348091890626757137914773048080151982788009808953349522971703676209072447919253736713943719839321930921001920443146832964494535806286153336758808764827052922284527987735369082658226155752758837734585788583920437031679967832798697874531506375848295306002069974292647012532975382657869395896549536084026643086849168707638035984652951756449232381922841508279043449553683642165895518852273616853752192626547082225232322662203349617421624450106130361133033050996977517456780759336980017504035553443204836636663583950658161718264375035034007950563418777684540446570742277682688819816930529249402141227674467861784042184664703273065772145626307008333021727910295689307897812592176340797189662547498298629041419687123412984210580325376481846316396566413701109848755348878790562296275295266190788880122151835567771665815565611863261470167857288685014242115505182159685753576612239477286620238583071292970734389580521730540789853959607322402465845627773409459421340250476125665859926003121138412497735360569 | 6658 |
6719 | 215006106257113223254503015023149432126193150293791416185445173578281597218315377296589584591228602041183907532584815068471747291177386898925622477208530115714962355294842135137890474394949339249259335407710018584480055157825387089416912233252714054247018216597994795059161567922302450277281351135838393171424038832688432240078361264161523904355539085927738753968157018550258476163852090826756157915705283413226000816151712543838581066281600650278690534719371112997393190721068136840596790525950480851370510277560248341182341805553054000587378384785994695875587394905226703149605689830257768229987714770949192483302583569799141079867597051190134078718011730508482542567284418838119000563443985593691221203060137047648713095502877775290062907208508727269017130916691676838817452529964938878349395785642430571852241837461604136374448443730175081889502056290512497717177577492736555784081731998565765598518104822516520340301701034123926767472784665776779480628821628279687651736198541330802238405154786248043073 | 3359 |
7487 | 26828803997912886929710867041891989490486893845712448833 | 197 |
8929 | 197107422273014301919781414466039325387889623676342705850752210599969 | 496 |
8969 | 10508537584872980049787749414505440238543661684506416445249892188329191267897669657242625405655025902294996965713681247700894953567276596965114308183649957469931262029470372188492494505614207827774171575432114297123003373257035070542940532411186322417809411123684246738342720455933424175399671044286557638075591 | 1121 |
9547 | 1621441292160739312484402643488810210953460916758334047593952342310982348899125523375207637304333778211869062392988099059802528019593682234941755422758885656395068722385037980657466257618112582188770921312100125511337836412531718154395821529210922389443733616354268820219577863577759459082447218927273695668223251258943006743614909639761127161704816862626236353032622115795192245125083091261029053988053316433377173895018793740052548266015018756763150731725385456332232982433576015547722563978072554378000015707071821371450842910648052930276764535303424167478747579771592484270800978561959411183367133498969236434846108865206764889977963554070295936092795484663326925724277620386077381551473009733178990983013487085676185144378484902884955972104873606558173086267499547566081780818064857671567480196001693236835136811036110768546793929610732909274227296407079545788520811837495181586420117807667033593394473 | 9546 |
Aunque hay 1228 primos impares por debajo de 10000, solo 21 de ellos son únicos y 76 de ellos son bi-únicos en binario.
Un ejemplo clásico de primos binarios binarios son
- 46817226351072265620777670675006972301618979214252832875068976303839400413682313921168154465151768472420980044715745858522803980473207943564433 (143 dígitos)
y
- 527739642811233917558838216073534609312522896254707972010583175760467054896492872702786549764052643493511382273226052631979775533936351462037464331880467187714178303247247247
son los dos factores primos del número de Mersenne 2 1061 −1. [5] Por lo tanto, la duración del período
es de 1061.
A octubre de 2016, el principal binario bi-único probable más grande conocido es , [6] tiene una
duración de período de 5240707 acciones con solo el número primo 75392810903.
De manera similar, podemos definir "primos tri-únicos" como un triple de primos que tienen una
longitud de período no compartida por otros primos. En binario, los primeros primos tri-únicos son:
primer p | los únicos otros dos primos que tienen el mismo período que p | duración del período |
---|---|---|
53 | 157, 1613 | 52 |
101 | 8101, 268501 | 100 |
103 | 2143, 11119 | 51 |
131 | 409891, 7623851 | 130 |
137 | 953, 26317 | 68 |
157 | 53, 1613 | 52 |
163 | 135433, 272010961 | 162 |
179 | 62020897, 18584774046020617 | 178 |
181 | 54001, 29247661 | 180 |
191 | 420778751, 30327152671 | 95 |
197 | 19707683773, 4981857697937 | 196 |
199 | 153649, 33057806959 | 99 |
211 | 664441, 1564921 | 210 |
229 | 457, 525313 | 76 |
233 | 1103, 2089 | 29 |
271 | 348031, 49971617830801 | 135 |
307 | 2857, 6529 | 102 |
317 | 381364611866507317969, 604462909806215075725313 | 316 |
359 | 1433, 1489459109360039866456940197095433721664951999121 | 179 |
367 | 55633, 37201708625305146303973352041 | 183 |
373 | 951088215727633, 4611545283086450689 | 372 |
419 | 3410623284654639440707, 1607792018780394024095514317003 | 418 |
421 | 146919792181, 1041815865690181 | 420 |
431 | 9719, 2099863 | 43 |
439 | 2298041, 9361973132609 | 73 |
443 | 4714692062809, 4507513575406446515845401458366741487526913 | 442 |
457 | 229, 525313 | 76 |
467 | 27961, 352369374013660139472574531568890678155040563007620742839120913 | 466 |
491 | 15162868758218274451, 50647282035796125885000330641 | 490 |
En binario, los primos n- únicos más pequeños son
- 3, 23, 53, 149, 269, 461, 619, 389, ...
En binario, la duración del período de los primos impares es: (secuencia A014664 en la OEIS )
principal | duración del período | principal | duración del período | principal | duración del período | principal | duración del período | principal | duración del período | principal | duración del período | principal | duración del período |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | 2 | 79 | 39 | 181 | 180 | 293 | 292 | 421 | 420 | 557 | 556 | 673 | 48 |
5 | 4 | 83 | 82 | 191 | 95 | 307 | 102 | 431 | 43 | 563 | 562 | 677 | 676 |
7 | 3 | 89 | 11 | 193 | 96 | 311 | 155 | 433 | 72 | 569 | 284 | 683 | 22 |
11 | 10 | 97 | 48 | 197 | 196 | 313 | 156 | 439 | 73 | 571 | 114 | 691 | 230 |
13 | 12 | 101 | 100 | 199 | 99 | 317 | 316 | 443 | 442 | 577 | 144 | 701 | 700 |
17 | 8 | 103 | 51 | 211 | 210 | 331 | 30 | 449 | 224 | 587 | 586 | 709 | 708 |
19 | 18 | 107 | 106 | 223 | 37 | 337 | 21 | 457 | 76 | 593 | 148 | 719 | 359 |
23 | 11 | 109 | 36 | 227 | 226 | 347 | 346 | 461 | 460 | 599 | 299 | 727 | 121 |
29 | 28 | 113 | 28 | 229 | 76 | 349 | 348 | 463 | 231 | 601 | 25 | 733 | 244 |
31 | 5 | 127 | 7 | 233 | 29 | 353 | 88 | 467 | 466 | 607 | 303 | 739 | 246 |
37 | 36 | 131 | 130 | 239 | 119 | 359 | 179 | 479 | 239 | 613 | 612 | 743 | 371 |
41 | 20 | 137 | 68 | 241 | 24 | 367 | 183 | 487 | 243 | 617 | 154 | 751 | 375 |
43 | 14 | 139 | 138 | 251 | 50 | 373 | 372 | 491 | 490 | 619 | 618 | 757 | 756 |
47 | 23 | 149 | 148 | 257 | dieciséis | 379 | 378 | 499 | 166 | 631 | 45 | 761 | 380 |
53 | 52 | 151 | 15 | 263 | 131 | 383 | 191 | 503 | 251 | 641 | 64 | 769 | 384 |
59 | 58 | 157 | 52 | 269 | 268 | 389 | 388 | 509 | 508 | 643 | 214 | 773 | 772 |
61 | 60 | 163 | 162 | 271 | 135 | 397 | 44 | 521 | 260 | 647 | 323 | 787 | 786 |
67 | 66 | 167 | 83 | 277 | 92 | 401 | 200 | 523 | 522 | 653 | 652 | 797 | 796 |
71 | 35 | 173 | 172 | 281 | 70 | 409 | 204 | 541 | 540 | 659 | 658 | 809 | 404 |
73 | 9 | 179 | 178 | 283 | 94 | 419 | 418 | 547 | 546 | 661 | 660 | 811 | 270 |
En binario, los números primos con una longitud de período determinada son: (secuencia A108974 en la OEIS )
duración del período | prima (s) | duración del período | prima (s) | duración del período | prima (s) | duración del período | prima (s) |
---|---|---|---|---|---|---|---|
1 | (ninguno) | 26 | 2731 | 51 | 103, 2143, 11119 | 76 | 229, 457, 525313 |
2 | 3 | 27 | 262657 | 52 | 53, 157, 1613 | 77 | 581283643249112959 |
3 | 7 | 28 | 29, 113 | 53 | 6361, 69431, 20394401 | 78 | 22366891 |
4 | 5 | 29 | 233, 1103, 2089 | 54 | 87211 | 79 | 2687, 202029703, 1113491139767 |
5 | 31 | 30 | 331 | 55 | 881, 3191, 201961 | 80 | 4278255361 |
6 | (ninguno) | 31 | 2147483647 | 56 | 15790321 | 81 | 2593, 71119, 97685839 |
7 | 127 | 32 | 65537 | 57 | 32377, 1212847 | 82 | 83, 8831418697 |
8 | 17 | 33 | 599479 | 58 | 59, 3033169 | 83 | 167, 57912614113275649087721 |
9 | 73 | 34 | 43691 | 59 | 179951, 3203431780337 | 84 | 1429, 14449 |
10 | 11 | 35 | 71, 122921 | 60 | 61 de 1321 | 85 | 9520972806333758431 |
11 | 23, 89 | 36 | 37, 109 | 61 | 2305843009213693951 | 86 | 2932031007403 |
12 | 13 | 37 | 223, 616318177 | 62 | 715827883 | 87 | 4177, 9857737155463 |
13 | 8191 | 38 | 174763 | 63 | 92737, 649657 | 88 | 353, 2931542417 |
14 | 43 | 39 | 79, 121369 | 64 | 641, 6700417 | 89 | 618970019642690137449562111 |
15 | 151 | 40 | 61681 | sesenta y cinco | 145295143558111 | 90 | 18837001 |
dieciséis | 257 | 41 | 13367, 164511353 | 66 | 67, 20857 | 91 | 911, 112901153, 23140471537 |
17 | 131071 | 42 | 5419 | 67 | 193707721, 761838257287 | 92 | 277, 1013, 1657, 30269 |
18 | 19 | 43 | 431, 9719, 2099863 | 68 | 137, 953, 26317 | 93 | 658812288653553079 |
19 | 524287 | 44 | 397, 2113 | 69 | 10052678938039 | 94 | 283, 165768537521 |
20 | 41 | 45 | 631, 23311 | 70 | 281, 86171 | 95 | 191, 420778751, 30327152671 |
21 | 337 | 46 | 2796203 | 71 | 228479, 48544121, 212885833 | 96 | 193, 22253377 |
22 | 683 | 47 | 2351, 4513, 13264529 | 72 | 433, 38737 | 97 | 11447, 13842607235828485645766393 |
23 | 47, 178481 | 48 | 97, 673 | 73 | 439, 2298041, 9361973132609 | 98 | 4363953127297 |
24 | 241 | 49 | 4432676798593 | 74 | 1777, 25781083 | 99 | 199, 153649, 33057806959 |
25 | 601, 1801 | 50 | 251, 4051 | 75 | 100801, 10567201 | 100 | 101, 8101, 268501 |
Duraciones de los períodos
Tabla de longitudes de período de 1 a 100 (los números primos únicos están en negrita) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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|
Prima única en varias bases
base | duración del período único (buscado hasta 4096) |
---|---|
2 | 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 54, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 147, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261, 280, 296, 312, 322, 334, 342, 345, 366, 374, 382, 398, 410, 414, 425, 447, 471, 507, 521, 550, 567, 579, 590, 600, 602, 607, 626, 690, 694, 712, 745, 795, 816, 889, 897, 909, 954, 990, 1106, 1192, 1224, 1230, 1279, 1384, 1386, 1402, 1464, 1512, 1554, 1562, 1600, 1670, 1683, 1727, 1781, 1834, 1904, 1990, 1992, 2008, 2037, 2203, 2281, 2298, 2353, 2406, 2456, 2499, 2536, 2838, 3006, 3074, 3217, 3415, 3418, 3481, 3766, 3817, 3927, ... |
3 | 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 20, 21, 24, 26, 32, 33, 36, 40, 46, 60, 63, 64, 70, 71, 72, 86, 103, 108, 128, 130, 132, 143, 145, 154, 161, 236, 255, 261, 276, 279, 287, 304, 364, 430, 464, 513, 528, 541, 562, 665, 672, 680, 707, 718, 747, 760, 782, 828, 875, 892, 974, 984, 987, 1037, 1058, 1070, 1073, 1080, 1091, 1154, 1248, 1367, 1426, 1440, 1462, 1524, 1598, 1623, 1627, 1863, 1985, 2132, 2188, 2196, 2340, 2460, 2508, 2626, 2640, 2739, 2856, 3092, 3158, 3262, 3315, 3326, 3482, 3638, 3982, 4018, 4036, ... |
4 | 1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 28, 40, 60, 92, 96, 104, 140, 148, 156, 300, 356, 408, 596, 612, 692, 732, 756, 800, 952, 996, 1004, 1228, 1268, 2240, 2532, 3060, 3796, 3824, 3944, ... |
5 | 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 18, 24, 28, 47, 48, 49, 56, 57, 88, 90, 92, 108, 110, 116, 120, 127, 134, 141, 149, 161, 171, 181, 198, 202, 206, 236, 248, 288, 357, 384, 420, 458, 500, 530, 536, 619, 620, 694, 798, 897, 929, 981, 992, 1064, 1134, 1230, 1670, 1807, 2094, 2162, 2369, 2516, 2649, 2988, 3407, 3888, ... |
6 | 1, 2, 3, 4, 5, 6, 7, 8, 18, 21, 22, 24, 29, 30, 42, 50, 62, 71, 86, 90, 94, 118, 124, 127, 129, 144, 154, 186, 192, 214, 271, 354, 360, 411, 480, 509, 558, 575, 663, 764, 814, 825, 874, 1028, 1049, 1050, 1102, 1113, 1131, 1158, 1376, 1464, 1468, 1535, 1622, 1782, 1834, 1924, 2096, 2176, 2409, 2464, 2816, 3013, 3438, 3453, 3663, ... |
7 | 3, 5, 6, 8, 13, 18, 21, 28, 30, 34, 36, 46, 48, 50, 54, 55, 58, 63, 76, 84, 94, 105, 122, 131, 148, 149, 224, 280, 288, 296, 332, 352, 456, 528, 531, 581, 650, 654, 730, 740, 759, 1026, 1047, 1065, 1460, 1660, 1699, 1959, 2067, 2260, 2380, 2665, 2890, 3238, 4020, ... |
8 | 1, 2, 3, 6, 9, 18, 30, 42, 78, 87, 114, 138, 189, 303, 318, 330, 408, 462, 504, 561, 1002, 1389, 1746, 1794, 2040, 2418, 2790, 3894, 4077, ... |
9 | 1, 2, 4, 6, 10, 12, 16, 18, 20, 30, 32, 36, 54, 64, 66, 118, 138, 152, 182, 232, 264, 336, 340, 380, 414, 446, 492, 540, 624, 720, 762, 1066, 1094, 1098, 1170, 1230, 1254, 1320, 1428, 1546, 2018, 2574, 2724, 2804, 2920, 3074, 3316, 3646, ... |
10 | 1, 2, 3, 4, 9, 10, 12, 14, 19, 23, 24, 36, 38, 39, 48, 62, 93, 106, 120, 134, 150, 196, 294, 317, 320, 385, 586, 597, 654, 738, 945, 1031, 1172, 1282, 1404, 1426, 1452, 1521, 1752, 1812, 1836, 1844, 1862, 2134, 2232, 2264, 2667, 3750, 3903, 3927, ... |
11 | 2, 4, 5, 6, 8, 9, 10, 14, 15, 17, 18, 19, 20, 27, 36, 42, 45, 52, 60, 73, 91, 104, 139, 205, 234, 246, 318, 358, 388, 403, 458, 552, 810, 855, 878, 907, 1114, 1131, 1220, 1272, 1431, 1470, 1568, 1614, 1688, 1696, 1907, 2029, 2136, 2288, 2535, 2577, ... |
12 | 1, 2, 3, 5, 10, 12, 19, 20, 21, 22, 56, 60, 63, 70, 80, 84, 92, 97, 109, 111, 123, 164, 189, 218, 276, 317, 353, 364, 386, 405, 456, 511, 636, 675, 701, 793, 945, 1090, 1268, 1272, 1971, 2088, 2368, 2482, 2893, 2966, 3290, ... |
13 | 2, 3, 5, 6, 7, 8, 9, 12, 16, 22, 24, 28, 33, 34, 38, 78, 80, 102, 137, 140, 147, 224, 230, 283, 304, 341, 360, 372, 384, 418, 420, 436, 483, 568, 570, 594, 737, 744, 855, 883, 991, 1021, 1193, 1222, 1615, 1628, 1838, 2032, 2146, 2302, 2530, 2830, 2958, 3030, 3528, 3671, 3885, ... |
14 | 1, 3, 4, 6, 7, 14, 19, 24, 31, 33, 35, 36, 41, 55, 60, 106, 114, 129, 152, 153, 172, 222, 265, 286, 400, 448, 560, 584, 864, 1006, 1335, 1363, 1520, 1536, 1659, 1862, 1925, 2332, 2458, 2687, 3381, 3512, 3870, 3976, ... |
15 | 3, 4, 6, 7, 14, 24, 43, 54, 58, 73, 85, 93, 102, 184, 220, 221, 228, 232, 247, 291, 305, 486, 487, 505, 551, 552, 590, 1029, 1194, 1274, 1406, 1444, 1532, 1548, 1748, 1986, 2093, 2182, 2202, 2579, 2781, 3054, 3239, 3696, ... |
dieciséis | 2, 4, 6, 8, 10, 14, 20, 30, 46, 48, 52, 70, 74, 78, 150, 178, 204, 298, 306, 346, 366, 378, 400, 476, 498, 502, 614, 634, 1120, 1266, 1530, 1898, 1912, 1972, 2548, 2770, 3738, 3850, ... |
17 | 1, 2, 3, 5, 7, 8, 11, 12, 14, 15, 34, 42, 46, 47, 48, 50, 71, 77, 94, 110, 114, 147, 154, 176, 228, 235, 258, 275, 338, 350, 419, 450, 480, 515, 589, 624, 666, 716, 724, 810, 815, 1232, 1490, 1934, 2106, 2391, 2732, 2904, 3462, 3912, 4053, ... |
18 | 1, 2, 3, 6, 14, 17, 21, 24, 30, 33, 38, 45, 46, 72, 78, 114, 146, 168, 288, 414, 440, 448, 665, 792, 801, 816, 975, 1165, 1176, 1267, 1466, 1513, 1882, 1920, 1998, 2194, 2272, 2643, 2800, 2946, 3434, 3504, 3813, 3866, 3957, ... |
19 | 2, 3, 4, 6, 19, 20, 31, 34, 47, 56, 59, 61, 70, 74, 91, 92, 96, 98, 107, 120, 145, 156, 168, 242, 276, 314, 326, 337, 387, 565, 602, 612, 892, 984, 1061, 1067, 1079, 1262, 1328, 2356, 3033, 3419, 3501, 3963, ... |
20 | 1, 3, 4, 6, 8, 9, 10, 11, 17, 30, 98, 100, 110, 126, 154, 158, 160, 168, 178, 182, 228, 266, 270, 280, 340, 416, 480, 574, 774, 980, 1052, 1139, 1338, 1418, 1474, 1487, 1594, 1902, 2326, 3112, 3520, 3808, 3830, ... |
21 | 2, 3, 5, 6, 8, 9, 10, 11, 14, 17, 26, 43, 64, 74, 81, 104, 192, 271, 321, 335, 348, 404, 437, 445, 516, 671, 694, 788, 1788, 1943, 2343, 2742, 3031, 3135, ... |
22 | 2, 5, 6, 7, 10, 21, 25, 26, 69, 79, 86, 93, 100, 101, 154, 158, 161, 171, 202, 214, 294, 354, 359, 424, 454, 602, 687, 706, 744, 857, 1028, 1074, 1136, 1150, 1345, 1408, 1525, 1572, 1578, 1988, 2142, 2665, ... |
23 | 2, 5, 8, 11, 15, 22, 26, 39, 42, 45, 54, 56, 132, 134, 145, 147, 196, 212, 218, 252, 343, 580, 662, 816, 820, 846, 1078, 1092, 1174, 1189, 1548, 1632, 2040, 2180, 2348, 2732, 3100, 3181, 4010, ... |
24 | 1, 2, 3, 4, 5, 8, 14, 19, 22, 38, 45, 53, 54, 70, 71, 117, 140, 144, 169, 186, 192, 195, 196, 430, 653, 661, 744, 834, 855, 870, 927, 1128, 1158, 1390, 1516, 1555, 1617, 1844, 2022, 2060, 2208, 2812, 3153, 3952, ... |
25 | 2, 4, 6, 12, 14, 24, 28, 44, 46, 54, 58, 60, 118, 124, 144, 192, 210, 250, 268, 310, 496, 532, 1258, 1494, 1944, 2050, 2498, 2728, 3324, 3418, 3646, 3862, 4014, ... |
26 | 1, 2, 4, 7, 9, 18, 20, 22, 24, 30, 43, 69, 132, 140, 186, 200, 210, 218, 267, 347, 454, 495, 554, 585, 645, 694, 980, 1028, 1060, 1098, 1432, 1714, 1828, 3513, 3786, ... |
27 | 2, 3, 12, 21, 24, 36, 87, 93, 171, 249, 276, 360, 480, 621, 732, 780, 1716, 3843, ... |
28 | 1, 2, 3, 5, 6, 8, 17, 21, 38, 81, 91, 96, 102, 132, 148, 156, 240, 258, 260, 276, 457, 464, 465, 500, 506, 535, 684, 746, 838, 930, 982, 1015, 1189, 1296, 1335, 1345, 1390, 1423, 2062, 2723, 2893, 3078, ... |
29 | 4, 5, 6, 7, 8, 14, 30, 32, 39, 45, 50, 76, 116, 151, 222, 357, 402, 462, 570, 588, 636, 671, 695, 844, 1498, 1650, 1770, 3175, 3195, 3312, 3538, 3719, ... |
30 | 1, 2, 5, 9, 11, 12, 21, 36, 51, 64, 91, 163, 174, 195, 230, 278, 318, 342, 346, 424, 530, 569, 578, 795, 984, 1094, 1167, 1335, 1564, 1605, 1658, 1789, 2159, 2204, 2225, 3366, 3458, 3615, ... |
31 | 3, 7, 12, 17, 24, 30, 31, 33, 40, 176, 218, 308, 404, 420, 630, 693, 890, 915, 922, 1475, 2122, 2185, 2487, 2541, 2907, 3387, 4055, ... |
32 | 1, 6, 30, 85, 110, 120, 320, 1050, 1065, 1385, 2490, 3080, 3920, ... |
33 | 1, 2, 3, 10, 16, 25, 28, 30, 35, 36, 45, 56, 76, 87, 110, 134, 135, 197, 200, 220, 228, 314, 324, 330, 396, 498, 583, 624, 725, 806, 940, 1145, 1240, 1644, 1750, 2171, 2268, 2675, 2781, 2790, 2808, 3581, ... |
34 | 3, 6, 8, 10, 13, 20, 24, 56, 87, 154, 164, 196, 282, 363, 428, 652, 744, 780, 860, 902, 952, 1178, 1493, 1540, 1643, 1904, 2184, 2277, 2468, 2943, ... |
35 | 2, 4, 6, 8, 18, 21, 22, 26, 42, 128, 154, 158, 170, 180, 184, 192, 254, 313, 450, 624, 737, 762, 798, 874, 912, 1002, 1006, 1098, 1234, 1297, 1418, 1714, 1926, 2325, 2343, 2368, 2998, 3567, 4064, ... |
36 | 2, 4, 12, 62, 72, 96, 180, 240, 382, 514, 688, 732, 734, 962, 1048, 1088, 1232, 1408, 2088, 2176, 2248, 2724, 3180, ... |
norte | bases tales que haya un número primo único con período n |
1 | 3, 4, 5, 6, 8, 10, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284, 294, 308, 312, 314, 318, 332, 338, 348, 350, 354, 360, 368, 374, 380, 384, 390, 398, 402, 410, 420, 422, 432, 434, 440, 444, 450, 458, 462, 464, 468, 480, 488, 492, 500, 504, 510, 522, 524, 542, 548, 558, 564, 570, 572, 578, 588, 594, 600, 602, 608, 614, 618, 620, 632, 642, 644, 648, 654, 660, 662, 674, 678, 684, 692, 702, 710, 720, 728, 734, 740, 744, 752, 758, 762, 770, 774, 788, 798, 810, 812, 822, 824, 828, 830, 840, 854, 858, 860, 864, 878, 882, 884, 888, 908, 912, 920, 930, 938, 942, 948, 954, 968, 972, 978, 984, 992, 998, 1010, 1014, 1020, 1022, 1032, 1034, 1040, 1050, 1052, 1062, 1064, 1070, 1088, 1092, 1094, 1098, 1104, 1110, 1118, 1124, 1130, 1152, 1154, 1164, 1172, 1182, 1188, 1194, 1202, 1214, 12 18, 1224, 1230, 1232, 1238, 1250, 1260, 1278, 1280, 1284, 1290, 1292, 1298, 1302, 1304, 1308, 1320, 1322, 1328, 1362, 1368, 1374, 1382, 1400, 1410, 1424, 1428, 1430, 1434, 1440, 1448, 1452, 1454, 1460, 1472, 1482, 1484, 1488, 1490, 1494, 1500, 1512, 1524, 1532, 1544, 1550, 1554, 1560, 1568, 1572, 1580, 1584, 1598, 1602, 1608, 1610, 1614, 1620, 1622, 1628, 1638, 1658, 1664, 1668, 1670, 1694, 1698, 1700, 1710, 1722, 1724, 1734, 1742, 1748, 1754, 1760, 1778, 1784, 1788, 1790, 1802, 1812, 1824, 1832, 1848, 1862, 1868, 1872, 1874, 1878, 1880, 1890, 1902, 1908, 1914, 1932, 1934, 1950, 1952, 1974, 1980, 1988, 1994, 1998, 2000, 2004, 2012, 2018, 2028, 2030, 2040, 2054, 2064, 2070, 2082, 2084, 2088, 2090, 2100, 2112, 2114, 2130, 2132, 2138, 2142, 2144, 2154, 2162, 2180, 2204, 2208, 2214, 2222, 2238, 2240, 2244, 2252, 2268, 2270, 2274, 2282, 2288, 2294, 2298, 2310, 2312, 2334, 2340, 2342, 2348, 2352, 2358, 2372, 2378, 2382, 2384, 2390, 2394, 2400, 2412, 2418, 2424, 2438, 2442, 2448, 2460, 2468, 2474, 2478, ... |
2 | 2, 4, 5, 6, 9, 10, 11, 12, 13, 16, 18, 19, 21, 22, 23, 25, 27, 28, 30, 33, 36, 37, 39, 40, 42, 43, 45, 46, 47, 51, 52, 55, 57, 58, 60, 61, 66, 67, 70, 72, 73, 75, 78, 79, 81, 82, 85, 87, 88, 91, 93, 95, 96, 100, 102, 103, 105, 106, 108, 111, 112, 115, 117, 121, 123, 126, 130, 133, 135, 136, 138, 141, 145, 147, 148, 150, 151, 156, 157, 159, 162, 163, 165, 166, 171, 172, 175, 177, 178, 180, 183, 187, 190, 191, 192, 193, 196, 198, 201, 205, 207, 210, 211, 213, 217, 222, 223, 225, 226, 228, 231, 232, 235, 238, 240, 243, 247, 250, 253, 256, 261, 262, 267, 268, 270, 271, 273, 276, 277, 280, 282, 283, 291, 292, 295, 297, 301, 303, 306, 310, 312, 313, 315, 316, 319, 325, 327, 330, 331, 333, 336, 343, 345, 346, 348, 351, 352, 355, 357, 358, 361, 366, 367, 372, 375, 378, 381, 382, 383, 385, 387, 388, 393, 396, 397, 400, 403, 408, 411, 415, 418, 420, 421, 423, 427, 430, 432, 435, 438, 442, 445, 447, 448, 451, 453, 456, 457, 460, 462, 463, 465, 466, 471, 477, 478, 481, 486, 487, 490, 495, 498, 501 , 502, 507, 508, 513, 520, 522, 523, 525, 535, 537, 540, 541, 543, 546, 547, 553, 555, 556, 561, 562, 565, 567, 568, 570, 576 , 583, 585, 586, 591, 592, 595, 598, 600, 603, 606, 607, 612, 613, 616, 618, 621, 625, 627, 630, 631, 633, 639, 640, 642, 646 , 651, 652, 655, 658, 660, 661, 663, 667, 672, 673, 676, 682, 687, 690, 691, 693, 697, 700, 703, 705, 708, 711, 715, 717, 718 , 723, 726, 732, 733, 735, 738, 742, 745, 750, 751, 756, 757, 760, 763, 765, 767, 768, 771, 772, 775, 777, 786, 787, 793, 795 , 796, 801, 807, 808, 810, 817, 820, 822, 823, 826, 828, 831, 837, 838, 841, 843, 847, 852, 855, 856, 858, 861, 862, 865, 871 , 876, 877, 880, 882, 885, 886, 891, 895, 897, 903, 906, 907, 910, 913, 915, 918, 921, 925, 927, 928, 931, 933, 936, 940, 943 , 946, 952, 955, 957, 963, 966, 970, 973, 975, 976, 981, 982, 990, 991, 996, 997, 1003, 1005, 1008, 1012, 1015, 1017, 1018, 1020, 1027 , 1030, 1032, 1038, 1041, 1045, 1047, 1048, 1050, 1051, 1060, 1062, 1068, 1071, 1075, 1081, 1083, 1086, 1087, 1090, 1092, 1093, 1095, 1096, 1102, 1107, 1108, 1111, 1113, 1116, 1122, 1123, 1125, 1128, 1131, 1135, 1137, 1141, 1150, 1152, 1153, 1162, 1167, 1170, 1171, 1173, 1180, 1183, 1185, 1186, 1191, 1192, 1197, 1200, 1201, 1207, 1212, 1213, 1215, 1216, 1222, 1225, 1227, 1228, 1230, 1233, 1236, 1237, 1243, 1248, 1251, 1255, 1258, 1261, 1263, 1267, 1276, 1278, 1279, 1281, 1282, 1285, 1288, 1290, 1293, 1296, 1300, 1302, 1303, 1305, 1306, 1311, 1317, 1318, 1320, 1321, 1323, 1326, 1327, 1335, 1345, 1347, 1353, 1360, 1365, 1366, 1372, 1375, 1380, 1381, 1383, 1387, 1395, 1398, 1401, 1407, 1408, 1411, 1417, 1422, 1423, 1426, 1428, 1431, 1432, 1435, 1437, 1438, 1446, 1447, 1450, 1452, 1453, 1458, 1465, 1467, 1470, 1471, 1477, 1480, 1482, 1485, 1486, 1488, 1491, 1492, 1498, 1501, 1503, 1510, 1513, 1515, 1521, 1522, 1527, 1530, 1531, 1535, 1537, 1542, 1543, 1545, 1548, 1551, 1552, 1555, 1558, 1566, 1570, 1573, 1575, 1578, 1582, 1587, 1591, 1593, 1596, 1600, 1603, 1606, 1608, 1612, 1615, 1617, 1618, 1620, 1621 1626, 1635, 1636, 1641, 1645, 1647, 1653, 1656, 1657, 1662, 1663, 1666, 1668, 1675, 1677, 1683, 1687, 1692, 1695, 1696, 1698, 1705, 1708, 1711, 1713 , 1717, 1720, 1722, 1723, 1725, 1731, 1732, 1740, 1743, 1746, 1752, 1753, 1755, 1758, 1761, 1765, 1771, 1773, 1776, 1782, 1783, 1786, 1788, 1791, 1795 , 1800, 1807, 1810, 1813, 1815, 1821, 1822, 1827, 1830, 1831, 1837, 1843, 1846, 1851, 1855, 1857, 1860, 1863, 1866, 1867, 1870, 1872, 1873, 1876, 1878 , 1881, 1887, 1888, 1893, 1900, 1905, 1906, 1911, 1912, 1915, 1927, 1930, 1932, 1933, 1941, 1947, 1948, 1950, 1951, 1953, 1963, 1965, 1972, 1978, 1981 , 1983, 1986, 1992, 1993, 1995, 1996, 1998, 2002, 2007, 2010, 2011, 2016, 2017, 2025, 2026, 2028, 2031, 2035, 2037, 2038, 2041, 2052, 2055, 2061, 2062 , 2065, 2068, 2077, 2080, 2082, 2083, 2086, 2088, 2091, 2095, 2097, 2098, 2101, 2103, 2110, 2112, 2121, 2125, 2128, 2130, 2136, 2137, 2140, 2142, 2143 , 2151, 2152, 2160, 2163, 2167, 2173, 2175, 2178, 2181, 2185, 2187, 2191, 2193, 2202, 2205, 2206, 22 12, 2215, 2217, 2220, 2223, 2227, 2233, 2236, 2238, 2242, 2245, 2247, 2250, 2251, 2257, 2263, 2266, 2268, 2271, 2272, 2275, 2280, 2283, 2286, 2292, 2296, 2301, 2305, 2307, 2308, 2310, 2325, 2332, 2335, 2338, 2340, 2341, 2343, 2346, 2347, 2350, 2356, 2361, 2367, 2370, 2371, 2373, 2376, 2380, 2382, 2383, 2385, 2388, 2392, 2395, 2398, 2401, 2403, 2410, 2415, 2416, 2422, 2425, 2427, 2431, 2433, 2436, 2440, 2445, 2446, 2451, 2455, 2457, 2458, 2461, 2466, 2467, 2472, 2473, 2475, 2476, 2487, 2497, ... |
3 | 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 17, 19, 20, 21, 24, 27, 28, 31, 33, 34, 38, 40, 41, 43, 50, 52, 54, 57, 59, 62, 66, 69, 70, 71, 73, 75, 76, 77, 78, 80, 82, 85, 89, 90, 91, 97, 99, 101, 103, 105, 110, 111, 112, 115, 117, 119, 124, 127, 131, 136, 138, 141, 143, 145, 147, 148, 150, 153, 155, 157, 161, 162, 164, 166, 167, 168, 173, 175, 176, 187, 188, 189, 190, 192, 194, 199, 202, 203, 206, 209, 215, 218, 223, 231, 236, 241, 244, 245, 246, 259, 265, 266, 271, 272, 274, 278, 279, 280, 286, 287, 288, 290, 293, 309, 314, 316, 325, 329, 332, 336, 342, 344, 348, 351, 357, 358, 369, 370, 376, 378, 381, 383, 385, 388, 392, 395, 398, 402, 404, 405, 409, 414, 416, 421, 426, 427, 434, 435, 442, 447, 453, 455, 456, 460, 469, 472, 475, 476, 489, 493, 495, 496, 500, 511, 512, 514, 517, 518, 525, 526, 530, 531, 533, 537, 538, 540, 551, 553, 554, 556, 559, 560, 566, 567, 572, 574, 579, 580, 582, 584, 586, 589, 603, 605, 609, 612, 616, 621, 622, 624, 626, 628, 635, 637, 642, 644, 649, 658, 661, 6 68, 671, 673, 677, 682, 686, 696, 700, 701, 712, 715, 720, 726, 727, 728, 735, 736, 743, 747, 754, 755, 761, 762, 768, 773, 775, 778, 782, 785, 792, 798, 799, 801, 812, 818, 819, 825, 827, 832, 836, 838, 839, 846, 850, 855, 857, 859, 860, 864, 868, 875, 878, 883, 889, 890, 894, 895, 897, 899, 910, 911, 915, 916, 918, 920, 922, 925, 927, 937, 943, 946, 950, 959, 960, 964, 969, 974, 981, 987, 990, 992, 993, 994, 1000, 1001, 1002, 1006, 1007, 1011, 1016, 1020, 1021, 1022, 1027, 1029, 1039, 1041, 1051, 1057, 1058, 1060, 1063, 1065, 1067, 1070, 1072, 1074, 1077, 1078, 1091, 1092, 1093, 1097, 1098, 1105, 1107, 1116, 1118, 1125, 1126, 1130, 1133, 1142, 1144, 1146, 1148, 1149, 1163, 1165, 1174, 1181, 1182, 1191, 1193, 1195, 1196, 1198, 1200, 1202, 1209, 1216, 1217, 1221, 1230, 1252, 1254, 1256, 1258, 1260, 1263, 1272, 1274, 1275, 1281, 1288, 1295, 1308, 1312, 1314, 1317, 1323, 1324, 1330, 1331, 1333, 1336, 1340, 1343, 1345, 1349, 1351, 1352, 1354, 1359, 1363, 1364, 1365, 1372, 1373, 1380, 1386 , 1392, 1396, 1401, 1405, 1414, 1415, 1421, 1422, 1427, 1434, 1438, 1440, 1441, 1442, 1443, 1447, 1448, 1449, 1454, 1456, 1473, 1475, 1483, 1484, 1487 , 1492, 1494, 1505, 1510, 1515, 1519, 1520, 1522, 1526, 1529, 1534, 1536, 1539, 1540, 1547, 1548, 1559, 1560, 1561, 1562, 1566, 1568, 1573, 1581, 1583 1585, 1590, 1592, 1594, 1596, 1609, 1611, 1616, 1620, 1624, 1630, 1632, 1639, 1644, 1646, 1650, 1651, 1657, 1658, 1659, 1665, 1666, 1669, 1672, 1676 , 1678, 1685, 1690, 1692, 1695, 1700, 1701, 1707, 1708, 1709, 1711, 1716, 1718, 1720, 1723, 1729, 1746, 1748, 1750, 1753, 1757, 1762, 1767, 1770, 1788 , 1795, 1800, 1804, 1806, 1809, 1811, 1814, 1818, 1825, 1826, 1828, 1832, 1837, 1841, 1847, 1848, 1853, 1861, 1863, 1879, 1882, 1886, 1895, 1902, 1909 , 1923, 1931, 1932, 1939, 1952, 1956, 1960, 1963, 1970, 1973, 1974, 1977, 1982, 1986, 1993, 1994, 1996, 2000, 2010, 2015, 2016, 2022, 2029, 2033, 2043 , 2049, 2054, 2056, 2058, 2064, 2065, 2068, 2073, 2075, 2079, 2080, 2085, 2086, 2091, 2105, 2107, 21 10, 2112, 2117, 2129, 2136, 2138, 2140, 2142, 2145, 2157, 2159, 2162, 2163, 2168, 2170, 2171, 2176, 2183, 2191, 2194, 2197, 2201, 2203, 2204, 2205, 2227, 2233, 2236, 2238, 2241, 2247, 2255, 2259, 2260, 2262, 2264, 2273, 2275, 2276, 2280, 2290, 2296, 2301, 2303, 2309, 2313, 2318, 2324, 2339, 2345, 2353, 2359, 2360, 2364, 2372, 2373, 2380, 2385, 2387, 2390, 2397, 2402, 2409, 2411, 2422, 2429, 2430, 2435, 2437, 2442, 2446, 2450, 2451, 2455, 2456, 2463, 2464, 2465, 2470, 2471, 2476, 2478, 2483, 2484, 2491, 2493, 2495, 2497, 2498, ... |
4 | 2, 3, 4, 5, 6, 9, 10, 11, 14, 15, 16, 19, 20, 24, 25, 26, 29, 35, 36, 39, 40, 45, 49, 51, 54, 56, 59, 61, 65, 66, 69, 71, 74, 79, 84, 85, 90, 94, 95, 101, 110, 116, 120, 121, 124, 126, 130, 131, 134, 139, 141, 145, 146, 150, 156, 159, 160, 165, 169, 170, 171, 175, 176, 180, 181, 184, 195, 199, 201, 204, 205, 206, 209, 210, 219, 221, 224, 230, 231, 236, 240, 245, 250, 256, 260, 261, 264, 270, 271, 275, 279, 280, 284, 289, 299, 300, 306, 309, 314, 315, 321, 325, 326, 329, 335, 340, 345, 349, 350, 371, 375, 379, 384, 386, 391, 396, 399, 400, 405, 406, 409, 415, 420, 425, 430, 435, 436, 440, 441, 444, 445, 449, 451, 459, 461, 464, 466, 470, 471, 474, 490, 496, 519, 521, 529, 535, 536, 544, 545, 556, 559, 569, 570, 571, 575, 576, 579, 581, 584, 594, 595, 609, 631, 634, 636, 639, 641, 644, 646, 649, 654, 661, 669, 674, 680, 685, 686, 689, 690, 695, 696, 699, 700, 704, 711, 714, 715, 716, 739, 740, 745, 750, 751, 760, 764, 779, 780, 781, 784, 791, 799, 815, 816, 819, 821, 826, 841, 855, 860, 861, 864, 869, 875, 881, 885, 890, 901, 906, 909, 910, 920, 921, 925, 929, 930, 935, 936, 946, 949, 950, 951, 955, 959, 960, 966, 979, 981, 985, 986, 989, 991, 1001, 1004, 1010, 1011, 1025, 1029, 1031, 1036, 1039, 1051, 1054, 1055, 1060, 1066, 1069, 1070, 1080, 1081, 1091, 1094, 1095, 1096, 1099, 1106, 1111, 1124, 1125, 1129, 1140, 1144, 1146, 1150, 1151, 1155, 1156, 1161, 1171, 1174, 1176, 1179, 1181, 1184, 1185, 1199, 1205, 1210, 1219, 1225, 1241, 1244, 1246, 1251, 1255, 1265, 1274, 1276, 1281, 1285, 1290, 1294, 1299, 1306, 1311, 1314, 1315, 1316, 1320, 1324, 1329, 1340, 1345, 1349, 1350, 1354, 1359, 1361, 1366, 1374, 1376, 1389, 1391, 1394, 1405, 1406, 1410, 1411, 1416, 1419, 1420, 1421, 1430, 1434, 1439, 1440, 1456, 1459, 1460, 1465, 1469, 1489, 1494, 1495, 1499, 1501, 1504, 1515, 1519, 1521, 1524, 1531, 1535, 1541, 1545, 1546, 1550, 1556, 1564, 1566, 1569, 1570, 1576, 1580, 1586, 1589, 1599, 1605, 1614, 1615, 1616, 1629, 1635, 1639, 1640, 1644, 1654, 1660, 1661, 1664, 1674, 1676, 1684, 1686, 1689, 1691, 1700, 1701, 1705, 1709, 1715, 1716, 1736, 1741, 1749, 1756, 1765, 1766, 1771, 1774, 1784, 1790, 1794, 1805, 1811, 1816, 1824, 1831, 1845, 1850, 1855, 1859, 1860, 1869, 1870, 1875, 1876, 1884, 1894, 1899, 1901, 1910, 1915, 1920, 1935, 1940, 1949, 1964, 1966, 1970, 1974, 1980, 1990, 2001, 2006, 2009, 2021, 2026, 2034, 2035, 2050, 2051, 2054, 2055, 2056, 2064, 2065, 2074, 2079, 2080, 2084, 2086, 2091, 2094, 2096, 2106, 2116, 2120, 2125, 2126, 2135, 2136, 2139, 2145, 2151, 2154, 2159, 2161, 2165, 2171, 2174, 2175, 2199, 2201, 2210, 2224, 2239, 2255, 2260, 2261, 2266, 2269, 2271, 2281, 2285, 2286, 2289, 2294, 2304, 2310, 2314, 2315, 2320, 2321, 2326, 2330, 2331, 2336, 2341, 2349, 2351, 2354, 2360, 2375, 2379, 2380, 2381, 2389, 2391, 2404, 2405, 2406, 2420, 2425, 2430, 2454, 2456, 2459, 2460, 2464, 2470, 2481, 2496, ... |
5 | 2, 3, 6, 7, 11, 12, 13, 17, 21, 22, 23, 24, 28, 29, 30, 40, 41, 43, 44, 46, 50, 56, 62, 63, 68, 73, 74, 77, 79, 83, 85, 94, 99, 110, 111, 117, 118, 120, 122, 127, 129, 134, 143, 145, 151, 154, 162, 164, 165, 166, 172, 175, 177, 186, 193, 198, 204, 206, 208, 222, 227, 239, 249, 254, 255, 260, 261, 263, 265, 274, 275, 276, 277, 285, 288, 292, 304, 308, 327, 336, 337, 340, 352, 359, 369, 373, 393, 397, 408, 414, 417, 418, 437, 439, 448, 457, 459, 474, 479, 486, 490, 492, 495, 496, 503, 505, 514, 519, 528, 530, 536, 538, 539, 540, 550, 556, 557, 561, 563, 567, 568, 572, 579, 594, 601, 604, 616, 617, 626, 637, 645, 650, 662, 679, 694, 699, 706, 711, 714, 728, 745, 750, 761, 765, 770, 772, 793, 804, 805, 824, 826, 837, 854, 860, 864, 868, 880, 886, 890, 891, 919, 921, 931, 936, 941, 942, 954, 967, 968, 974, 976, 979, 986, 991, 1001, 1007, 1009, 1044, 1045, 1047, 1053, 1066, 1078, 1079, 1085, 1102, 1108, 1111, 1129, 1133, 1135, 1152, 1154, 1157, 1173, 1178, 1183, 1187, 1201, 1209, 1228, 1239, 1249, 1251, 1253, 1266, 1276, 1282, 1284, 1297, 1327, 1333, 1343, 1348, 1352, 1370, 1377, 1382, 1396, 1398, 1416, 1419, 1426, 1429, 1452, 1462, 1463, 1475, 1480, 1481, 1493, 1503, 1506, 1520, 1525, 1536, 1553, 1557, 1562, 1563, 1579, 1596, 1641, 1646, 1657, 1662, 1663, 1668, 1672, 1679, 1683, 1684, 1694, 1695, 1696, 1704, 1746, 1748, 1749, 1755, 1760, 1762, 1767, 1770, 1788, 1826, 1836, 1838, 1843, 1859, 1881, 1883, 1891, 1914, 1921, 1927, 1944, 1947, 1960, 1975, 1977, 1979, 1981, 1987, 1990, 1991, 2021, 2032, 2034, 2037, 2041, 2052, 2059, 2069, 2076, 2080, 2086, 2090, 2097, 2098, 2111, 2118, 2123, 2131, 2134, 2164, 2167, 2175, 2177, 2218, 2228, 2233, 2243, 2245, 2252, 2261, 2272, 2274, 2289, 2295, 2299, 2300, 2305, 2318, 2321, 2328, 2332, 2340, 2356, 2361, 2362, 2366, 2373, 2375, 2382, 2383, 2387, 2430, 2431, 2432, 2438, 2448, 2450, 2464, 2483, 2487, 2499, ... |
6 | 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 18, 20, 21, 22, 25, 28, 29, 32, 34, 35, 39, 41, 42, 44, 51, 53, 55, 58, 60, 63, 67, 70, 71, 72, 74, 76, 77, 78, 79, 81, 83, 86, 90, 91, 92, 98, 100, 102, 104, 106, 111, 112, 113, 116, 118, 120, 125, 128, 132, 137, 139, 142, 144, 146, 148, 149, 151, 154, 156, 158, 162, 163, 165, 167, 168, 169, 174, 176, 177, 188, 189, 190, 191, 193, 195, 200, 203, 204, 207, 210, 216, 219, 224, 232, 237, 242, 245, 246, 247, 260, 266, 267, 272, 273, 275, 279, 280, 281, 287, 288, 289, 291, 294, 310, 315, 317, 326, 330, 333, 337, 343, 345, 349, 352, 358, 359, 370, 371, 377, 379, 382, 384, 386, 389, 393, 396, 399, 403, 405, 406, 410, 415, 417, 422, 427, 428, 435, 436, 443, 448, 454, 456, 457, 461, 470, 473, 476, 477, 490, 494, 496, 497, 501, 512, 513, 515, 518, 519, 526, 527, 531, 532, 534, 538, 539, 541, 552, 554, 555, 557, 560, 561, 567, 568, 573, 575, 580, 581, 583, 585, 587, 590, 604, 606, 610, 613, 617, 622, 623, 625, 627, 629, 636, 638, 643, 645, 650, 659, 662, 669, 672, 674, 678, 683, 687, 697, 701, 702, 713, 716, 721, 727, 728, 729, 736, 737, 744, 748, 755, 756, 762, 763, 769, 774, 776, 779, 783, 786, 793, 799, 800, 802, 813, 819, 820, 826, 828, 833, 837, 839, 840, 847, 851, 856, 858, 860, 861, 865, 869, 876, 879, 884, 890, 891, 895, 896, 898, 900, 911, 912, 916, 917, 919, 921, 923, 926, 928, 938, 944, 947, 951, 960, 961, 965, 970, 975, 982, 988, 991, 993, 994, 995, 1001, 1002, 1003, 1007, 1008, 1012, 1017, 1021, 1022, 1023, 1028, 1030, 1040, 1042, 1052, 1058, 1059, 1061, 1064, 1066, 1068, 1071, 1073, 1075, 1078, 1079, 1092, 1093, 1094, 1098, 1099, 1106, 1108, 1117, 1119, 1126, 1127, 1131, 1134, 1143, 1145, 1147, 1149, 1150, 1164, 1166, 1175, 1182, 1183, 1192, 1194, 1196, 1197, 1199, 1201, 1203, 1210, 1217, 1218, 1222, 1231, 1253, 1255, 1257, 1259, 1261, 1264, 1273, 1275, 1276, 1282, 1289, 1296, 1309, 1313, 1315, 1318, 1324, 1325, 1331, 1332, 1334, 1337, 1341, 1344, 1346, 1350, 1352, 1353, 1355, 1360, 1364, 1365, 1366, 1373, 1374, 1381, 138 7, 1393, 1397, 1402, 1406, 1415, 1416, 1422, 1423, 1428, 1435, 1439, 1441, 1442, 1443, 1444, 1448, 1449, 1450, 1455, 1457, 1474, 1476, 1484, 1485, 1488, 1493, 1495, 1506, 1511, 1516, 1520, 1521, 1523, 1527, 1530, 1535, 1537, 1540, 1541, 1548, 1549, 1560, 1561, 1562, 1563, 1567, 1569, 1574, 1582, 1584, 1586, 1591, 1593, 1595, 1597, 1610, 1612, 1617, 1621, 1625, 1631, 1633, 1640, 1645, 1647, 1651, 1652, 1658, 1659, 1660, 1666, 1667, 1670, 1673, 1677, 1679, 1686, 1691, 1693, 1696, 1701, 1702, 1708, 1709, 1710, 1712, 1717, 1719, 1721, 1724, 1730, 1747, 1749, 1751, 1754, 1758, 1763, 1768, 1771, 1789, 1796, 1801, 1805, 1807, 1810, 1812, 1815, 1819, 1826, 1827, 1829, 1833, 1838, 1842, 1848, 1849, 1854, 1862, 1864, 1880, 1883, 1887, 1896, 1903, 1910, 1924, 1932, 1933, 1940, 1953, 1957, 1961, 1964, 1971, 1974, 1975, 1978, 1983, 1987, 1994, 1995, 1997, 2001, 2011, 2016, 2017, 2023, 2030, 2034, 2044, 2050, 2055, 2057, 2059, 2065, 2066, 2069, 2074, 2076, 2080, 2081, 2086, 2087, 2092, 2106, 2108, 2 111, 2113, 2118, 2130, 2137, 2139, 2141, 2143, 2146, 2158, 2160, 2163, 2164, 2169, 2171, 2172, 2177, 2184, 2192, 2195, 2198, 2202, 2204, 2205, 2206, 2228, 2234, 2237, 2239, 2242, 2248, 2256, 2260, 2261, 2263, 2265, 2274, 2276, 2277, 2281, 2291, 2297, 2302, 2304, 2310, 2314, 2319, 2325, 2340, 2346, 2354, 2360, 2361, 2365, 2373, 2374, 2381, 2386, 2388, 2391, 2398, 2403, 2410, 2412, 2423, 2430, 2431, 2436, 2438, 2443, 2447, 2451, 2452, 2456, 2457, 2464, 2465, 2466, 2471, 2472, 2477, 2479, 2484, 2485, 2492, 2494, 2496, 2498, 2499, ... |
7 | 2, 3, 5, 6, 13, 14, 15, 17, 22, 26, 29, 31, 38, 40, 46, 50, 56, 60, 61, 66, 68, 72, 73, 80, 85, 87, 89, 93, 95, 115, 120, 122, 126, 128, 134, 146, 149, 156, 158, 160, 163, 180, 186, 192, 203, 206, 208, 220, 221, 235, 237, 238, 246, 251, 264, 266, 267, 280, 282, 290, 294, 300, 303, 309, 320, 330, 341, 349, 350, 351, 353, 363, 381, 395, 399, 404, 405, 414, 417, 418, 421, 436, 438, 447, 450, 461, 464, 466, 470, 478, 505, 519, 523, 531, 533, 539, 548, 560, 583, 584, 589, 591, 599, 609, 611, 622, 638, 646, 647, 655, 657, 660, 681, 698, 700, 701, 710, 717, 734, 760, 765, 776, 798, 800, 802, 805, 820, 822, 842, 855, 856, 862, 863, 869, 870, 878, 899, 911, 912, 913, 926, 927, 931, 940, 941, 942, 947, 959, 984, 998, 1016, 1023, 1029, 1046, 1052, 1055, 1081, 1084, 1087, 1111, 1115, 1117, 1131, 1136, 1144, 1148, 1161, 1169, 1170, 1188, 1189, 1194, 1195, 1197, 1221, 1224, 1229, 1248, 1266, 1277, 1280, 1281, 1284, 1291, 1297, 1309, 1316, 1333, 1339, 1348, 1363, 1364, 1371, 1377, 1382, 1402, 1404, 1 409, 1418, 1419, 1424, 1425, 1436, 1438, 1439, 1455, 1469, 1471, 1480, 1482, 1489, 1494, 1512, 1513, 1520, 1529, 1537, 1547, 1550, 1554, 1558, 1563, 1565, 1566, 1567, 1572, 1579, 1585, 1596, 1604, 1605, 1606, 1608, 1609, 1622, 1627, 1630, 1651, 1668, 1672, 1679, 1687, 1700, 1708, 1710, 1714, 1716, 1738, 1750, 1753, 1757, 1758, 1762, 1766, 1772, 1783, 1790, 1796, 1797, 1800, 1802, 1808, 1816, 1831, 1835, 1839, 1840, 1854, 1855, 1885, 1888, 1899, 1904, 1911, 1915, 1918, 1920, 1929, 1940, 1941, 1958, 1978, 1985, 1990, 1998, 2015, 2039, 2057, 2071, 2072, 2087, 2094, 2097, 2100, 2115, 2126, 2127, 2131, 2139, 2151, 2152, 2156, 2157, 2158, 2159, 2164, 2181, 2186, 2188, 2190, 2193, 2201, 2205, 2219, 2222, 2226, 2230, 2232, 2244, 2245, 2265, 2274, 2293, 2299, 2303, 2306, 2308, 2321, 2359, 2378, 2404, 2408, 2409, 2416, 2436, 2437, 2440, 2450, 2458, 2463, 2466, 2480, 2491, 2493, 2496, ... |
8 | 2, 3, 4, 5, 6, 7, 11, 13, 16, 17, 20, 21, 23, 24, 28, 29, 34, 35, 39, 46, 48, 54, 56, 57, 61, 65, 71, 73, 74, 80, 81, 82, 88, 90, 103, 105, 106, 113, 115, 118, 119, 129, 132, 140, 142, 153, 154, 160, 164, 165, 169, 171, 174, 180, 194, 198, 199, 203, 204, 205, 210, 220, 228, 238, 242, 248, 251, 254, 259, 266, 267, 272, 275, 276, 278, 288, 296, 309, 312, 313, 317, 320, 328, 333, 334, 337, 339, 340, 352, 353, 363, 364, 374, 403, 405, 414, 415, 419, 430, 431, 436, 442, 445, 449, 453, 455, 463, 466, 471, 472, 476, 477, 479, 487, 488, 492, 494, 498, 503, 504, 505, 513, 516, 517, 523, 526, 537, 539, 540, 543, 550, 551, 554, 556, 561, 566, 567, 568, 573, 579, 582, 584, 600, 605, 607, 613, 616, 623, 624, 628, 639, 643, 649, 656, 657, 677, 681, 690, 701, 702, 703, 710, 713, 719, 721, 725, 730, 732, 738, 742, 745, 748, 758, 760, 761, 768, 769, 772, 778, 786, 788, 795, 798, 800, 805, 810, 811, 819, 821, 829, 833, 843, 845, 855, 856, 857, 874, 879, 883, 891, 894, 895, 912, 913, 914, 917, 919, 928, 930, 931, 936, 952, 962, 963, 965, 966, 986, 992, 996, 997, 1007, 1013, 1015, 1019, 1038, 1041, 1042, 1047, 1049, 1053, 1057, 1071, 1072, 1076, 1087, 1088, 1089, 1101, 1119, 1123, 1125, 1126, 1132, 1135, 1136, 1142, 1144, 1150, 1152, 1163, 1170, 1173, 1180, 1183, 1200, 1202, 1218, 1236, 1238, 1246, 1252, 1253, 1259, 1269, 1270, 1275, 1280, 1302, 1305, 1322, 1327, 1330, 1333, 1344, 1353, 1355, 1371, 1381, 1382, 1383, 1388, 1389, 1401, 1404, 1406, 1428, 1434, 1441, 1442, 1446, 1457, 1458, 1463, 1472, 1483, 1485, 1486, 1493, 1496, 1527, 1529, 1533, 1536, 1540, 1542, 1547, 1552, 1554, 1557, 1558, 1567, 1568, 1569, 1571, 1586, 1594, 1598, 1610, 1612, 1618, 1622, 1635, 1638, 1644, 1646, 1650, 1652, 1655, 1666, 1680, 1683, 1687, 1688, 1700, 1706, 1710, 1718, 1722, 1737, 1738, 1745, 1751, 1754, 1755, 1757, 1765, 1772, 1788, 1789, 1806, 1809, 1813, 1820, 1823, 1824, 1829, 1836, 1841, 1849, 1850, 1853, 1854, 1864, 1865, 1870, 1892, 1905, 1909, 1910, 1915, 1916, 1926, 1932, 1934, 1935, 1942, 1944 , 1945, 1948, 1952, 1956, 1962, 1967, 1972, 1977, 1978, 1985, 1986, 1994, 2001, 2007, 2011, 2013, 2037, 2039, 2040, 2044, 2046, 2051, 2058, 2061, 2068 , 2069, 2071, 2073, 2074, 2079, 2097, 2102, 2104, 2108, 2125, 2126, 2131, 2141, 2142, 2143, 2145, 2149, 2152, 2158, 2162, 2163, 2175, 2192, 2193, 2204 , 2205, 2206, 2209, 2215, 2222, 2223, 2224, 2226, 2238, 2240, 2245, 2247, 2250, 2254, 2255, 2256, 2260, 2261, 2266, 2279, 2283, 2292, 2296, 2305, 2311 , 2312, 2315, 2322, 2333, 2336, 2341, 2343, 2349, 2350, 2360, 2363, 2368, 2369, 2373, 2374, 2376, 2384, 2397, 2400, 2403, 2408, 2414, 2421, 2428, 2432 , 2436, 2438, 2441, 2443, 2445, 2447, 2465, 2478, 2479, 2481, 2482, 2486, 2488, 2493, ... |
9 | 2, 3, 8, 10, 11, 13, 20, 21, 26, 30, 50, 51, 56, 60, 67, 76, 78, 88, 91, 98, 102, 117, 129, 134, 146, 154, 159, 163, 171, 186, 189, 190, 191, 193, 198, 200, 209, 210, 212, 222, 240, 249, 250, 265, 267, 269, 278, 279, 299, 300, 307, 333, 344, 363, 383, 388, 390, 398, 399, 406, 425, 429, 436, 438, 439, 444, 450, 458, 496, 504, 509, 520, 523, 533, 540, 544, 570, 580, 585, 603, 634, 637, 646, 658, 666, 668, 691, 698, 704, 716, 721, 735, 748, 798, 806, 809, 818, 827, 844, 866, 875, 886, 887, 889, 894, 939, 952, 962, 984, 989, 998, 1001, 1002, 1003, 1021, 1025, 1029, 1040, 1041, 1044, 1064, 1072, 1075, 1102, 1121, 1139, 1152, 1153, 1186, 1188, 1198, 1207, 1224, 1227, 1234, 1235, 1247, 1264, 1268, 1276, 1280, 1285, 1286, 1287, 1300, 1305, 1314, 1331, 1349, 1364, 1399, 1400, 1408, 1409, 1420, 1427, 1432, 1445, 1447, 1473, 1484, 1512, 1519, 1527, 1557, 1560, 1569, 1577, 1590, 1591, 1609, 1614, 1618, 1626, 1630, 1641, 1649, 1654, 1664, 1682, 1685, 1687, 1692, 1704, 1706, 1717, 1739, 1741, 1761, 1769, 1774, 1787, 1805, 1806, 1813, 1826, 1843, 1850, 1865, 1870, 1873, 1907, 1910, 1915, 1937, 1949, 1950, 1959, 1976, 1984, 1990, 2016, 2021, 2029, 2040, 2059, 2062, 2065, 2073, 2082, 2085, 2112, 2124, 2136, 2139, 2141, 2160, 2167, 2174, 2200, 2203, 2223, 2243, 2257, 2276, 2287, 2288, 2298, 2302, 2307, 2339, 2345, 2350, 2357, 2363, 2390, 2395, 2397, 2405, 2406, 2424, 2428, 2440, 2463, 2466, 2469, 2477, 2480, 2497, ... |
10 | 2, 3, 4, 5, 9, 10, 11, 12, 16, 20, 21, 22, 33, 34, 37, 38, 43, 47, 48, 55, 59, 69, 71, 75, 76, 80, 81, 99, 109, 111, 121, 124, 126, 131, 133, 135, 136, 141, 144, 155, 157, 158, 164, 165, 176, 177, 180, 199, 203, 223, 229, 242, 245, 251, 253, 254, 256, 257, 258, 264, 265, 268, 274, 276, 286, 290, 297, 307, 319, 322, 323, 334, 342, 361, 363, 366, 374, 375, 377, 385, 388, 396, 411, 427, 438, 439, 444, 452, 462, 483, 487, 489, 495, 499, 500, 505, 506, 507, 509, 510, 528, 531, 539, 549, 551, 555, 583, 584, 588, 603, 606, 609, 610, 628, 639, 641, 642, 652, 654, 658, 664, 676, 693, 702, 704, 707, 714, 716, 719, 738, 741, 749, 758, 760, 768, 774, 782, 791, 792, 812, 813, 815, 836, 839, 850, 861, 874, 894, 901, 912, 924, 935, 949, 960, 973, 978, 980, 982, 994, 1004, 1012, 1023, 1026, 1035, 1039, 1045, 1054, 1057, 1065, 1066, 1068, 1071, 1087, 1093, 1094, 1105, 1109, 1116, 1127, 1137, 1148, 1155, 1156, 1158, 1160, 1165, 1166, 1178, 1187, 1191, 1199, 1204, 1215, 1219, 1230, 1243, 1244, 1254, 1259 , 1265, 1266, 1270, 1276, 1279, 1281, 1291, 1310, 1320, 1341, 1342, 1353, 1364, 1365, 1368, 1374, 1375, 1401, 1433, 1452, 1462, 1473, 1474, 1475, 1488 , 1496, 1506, 1530, 1539, 1541, 1550, 1551, 1554, 1560, 1567, 1574, 1585, 1593, 1594, 1598, 1605, 1609, 1611, 1615, 1618, 1621, 1637, 1643, 1649, 1659 , 1660, 1661, 1676, 1686, 1692, 1695, 1698, 1715, 1716, 1717, 1719, 1738, 1752, 1754, 1761, 1775, 1780, 1791, 1805, 1818, 1819, 1831, 1838, 1840, 1842 , 1846, 1848, 1864, 1869, 1873, 1874, 1884, 1901, 1903, 1919, 1923, 1926, 1928, 1929, 1935, 1940, 1946, 1947, 1948, 1962, 1970, 1974, 1990, 1996, 2017 , 2023, 2025, 2046, 2058, 2066, 2080, 2099, 2102, 2111, 2112, 2124, 2134, 2143, 2160, 2165, 2170, 2189, 2192, 2210, 2222, 2227, 2232, 2233, 2256, 2258 , 2264, 2265, 2271, 2275, 2293, 2303, 2304, 2314, 2320, 2324, 2326, 2330, 2332, 2333, 2335, 2343, 2353, 2366, 2386, 2390, 2392, 2419, 2440, 2457, 2463 , 2469, 2473, 2484, ... |
11 | 5, 17, 20, 21, 23, 30, 53, 60, 86, 137, 172, 195, 212, 224, 229, 254, 258, 268, 272, 287, 298, 319, 339, 355, 365, 366, 389, 390, 398, 414, 467, 474, 480, 504, 534, 539, 543, 562, 567, 592, 619, 626, 654, 672, 709, 735, 756, 766, 770, 778, 787, 806, 812, 874, 943, 973, 1003, 1036, 1040, 1065, 1091, 1103, 1167, 1194, 1210, 1213, 1239, 1243, 1249, 1264, 1309, 1311, 1341, 1348, 1357, 1377, 1425, 1433, 1437, 1448, 1449, 1459, 1486, 1510, 1528, 1575, 1586, 1601, 1631, 1661, 1696, 1698, 1701, 1748, 1770, 1840, 1859, 1860, 1864, 1874, 1910, 1924, 1926, 1937, 1942, 1954, 1977, 1985, 1993, 2000, 2029, 2039, 2087, 2089, 2123, 2149, 2167, 2215, 2223, 2228, 2238, 2261, 2274, 2294, 2301, 2307, 2311, 2319, 2320, 2323, 2338, 2388, 2393, 2403, 2416, 2438, 2457, 2458, 2461, ... |
12 | 2, 3, 4, 5, 9, 10, 12, 13, 17, 25, 27, 30, 31, 36, 38, 39, 43, 48, 52, 55, 56, 61, 62, 65, 83, 92, 94, 99, 100, 104, 105, 109, 114, 118, 126, 131, 166, 168, 169, 172, 183, 185, 190, 194, 196, 198, 209, 224, 225, 229, 231, 239, 244, 257, 260, 261, 263, 269, 270, 272, 278, 291, 296, 299, 300, 302, 308, 311, 313, 320, 324, 328, 329, 339, 343, 346, 348, 350, 363, 374, 376, 390, 407, 412, 413, 417, 424, 426, 429, 434, 437, 438, 443, 447, 455, 463, 468, 480, 482, 485, 494, 502, 503, 507, 511, 515, 525, 533, 534, 545, 549, 555, 558, 559, 568, 571, 582, 593, 595, 599, 610, 612, 614, 619, 625, 632, 638, 640, 641, 647, 653, 659, 676, 684, 686, 697, 699, 701, 702, 707, 710, 716, 718, 724, 725, 729, 738, 742, 749, 767, 768, 777, 780, 793, 794, 797, 798, 801, 805, 811, 820, 832, 836, 840, 842, 853, 854, 861, 862, 868, 871, 872, 876, 893, 905, 909, 915, 923, 924, 949, 953, 958, 959, 961, 963, 967, 972, 974, 978, 988, 1000, 1009, 1015, 1018, 1026, 1031, 1036, 1039, 1040, 1045, 1063, 1067, 1070, 1074, 1080, 1101, 1105, 1110, 1113, 1122, 1123, 1126, 1132, 1134, 1135, 1147, 1156, 1174, 1195, 1196, 1205, 1208, 1210, 1212, 1214, 1219, 1232, 1239, 1251, 1256, 1258, 1261, 1275, 1284, 1299, 1305, 1308, 1325, 1326, 1331, 1336, 1344, 1360, 1365, 1369, 1370, 1373, 1375, 1379, 1394, 1395, 1405, 1413, 1416, 1421, 1426, 1434, 1440, 1452, 1459, 1460, 1464, 1473, 1483, 1486, 1490, 1491, 1492, 1499, 1505, 1516, 1517, 1521, 1524, 1538, 1550, 1552, 1555, 1563, 1569, 1572, 1576, 1589, 1590, 1596, 1598, 1600, 1611, 1616, 1624, 1625, 1635, 1641, 1647, 1652, 1654, 1659, 1660, 1661, 1663, 1669, 1680, 1689, 1690, 1693, 1695, 1700, 1704, 1712, 1713, 1717, 1719, 1726, 1733, 1739, 1741, 1746, 1751, 1756, 1758, 1759, 1764, 1773, 1778, 1780, 1789, 1793, 1811, 1823, 1829, 1830, 1832, 1841, 1854, 1856, 1860, 1863, 1875, 1885, 1886, 1889, 1890, 1893, 1897, 1898, 1899, 1902, 1914, 1915, 1927, 1928, 1929, 1933, 1936, 1949, 1951, 1963, 1967, 1971, 1980, 1986, 1989, 2005, 2011, 2018, 2033, 2037, 2040, 2054, 2055, 206 2, 2072, 2075, 2076, 2083, 2084, 2089, 2090, 2096, 2102, 2105, 2107, 2111, 2116, 2119, 2122, 2135, 2144, 2153, 2155, 2168, 2183, 2189, 2211, 2224, 2232, 2235, 2241, 2250, 2252, 2257, 2258, 2259, 2261, 2270, 2285, 2300, 2301, 2309, 2313, 2319, 2331, 2337, 2340, 2341, 2356, 2363, 2369, 2371, 2384, 2387, 2392, 2395, 2396, 2401, 2426, 2440, 2443, 2453, 2454, 2457, 2486, 2488, 2497, 2500, ... |
13 | 2, 3, 5, 7, 34, 37, 43, 59, 72, 92, 94, 98, 110, 118, 133, 149, 151, 159, 190, 207, 219, 221, 251, 260, 264, 267, 274, 282, 286, 291, 319, 355, 363, 373, 382, 397, 398, 402, 406, 408, 412, 436, 442, 443, 486, 489, 507, 542, 544, 552, 553, 573, 582, 585, 592, 603, 610, 614, 634, 643, 645, 677, 689, 708, 720, 730, 744, 769, 772, 806, 851, 853, 862, 882, 912, 928, 930, 952, 968, 993, 1006, 1019, 1025, 1040, 1047, 1067, 1097, 1098, 1120, 1125, 1131, 1133, 1153, 1165, 1172, 1175, 1191, 1197, 1236, 1245, 1248, 1262, 1271, 1273, 1275, 1281, 1299, 1305, 1306, 1311, 1346, 1376, 1378, 1400, 1403, 1404, 1412, 1418, 1428, 1431, 1442, 1450, 1471, 1496, 1502, 1570, 1585, 1587, 1660, 1662, 1666, 1736, 1754, 1757, 1836, 1853, 1860, 1861, 1885, 1903, 1913, 1915, 1972, 1975, 1987, 1988, 1995, 2006, 2033, 2052, 2073, 2098, 2191, 2193, 2206, 2210, 2224, 2252, 2255, 2267, 2280, 2302, 2314, 2319, 2324, 2346, 2362, 2366, 2417, 2444, 2450, 2479, 2486, ... |
14 | 2, 3, 10, 11, 14, 15, 16, 17, 18, 21, 24, 25, 29, 37, 43, 44, 46, 48, 49, 52, 54, 61, 66, 69, 72, 73, 78, 84, 86, 87, 99, 101, 104, 106, 114, 115, 128, 133, 135, 136, 143, 145, 146, 148, 164, 169, 170, 173, 200, 219, 224, 226, 228, 231, 234, 240, 244, 248, 255, 262, 275, 281, 282, 298, 301, 305, 320, 321, 322, 327, 330, 339, 347, 359, 363, 368, 369, 384, 385, 387, 401, 417, 433, 435, 442, 450, 455, 458, 482, 488, 494, 496, 508, 517, 519, 521, 553, 559, 566, 579, 582, 590, 601, 616, 621, 625, 628, 630, 636, 638, 654, 657, 669, 675, 691, 692, 694, 711, 712, 714, 719, 724, 725, 728, 732, 737, 750, 756, 757, 765, 768, 773, 774, 778, 780, 793, 797, 803, 810, 827, 828, 831, 842, 848, 860, 865, 869, 895, 901, 910, 916, 919, 922, 923, 926, 931, 936, 938, 951, 960, 967, 971, 972, 982, 1002, 1010, 1022, 1032, 1060, 1063, 1070, 1073, 1074, 1089, 1098, 1105, 1109, 1110, 1123, 1128, 1130, 1131, 1132, 1138, 1147, 1160, 1178, 1179, 1184, 1189, 1190, 1207, 1216, 1218, 1220, 1221, 1291, 1293, 1302, 130 3, 1308, 1332, 1349, 1350, 1353, 1357, 1361, 1362, 1366, 1373, 1374, 1386, 1394, 1407, 1435, 1448, 1474, 1487, 1511, 1515, 1524, 1535, 1538, 1558, 1562, 1563, 1564, 1581, 1597, 1605, 1614, 1615, 1616, 1626, 1638, 1639, 1645, 1648, 1653, 1654, 1671, 1681, 1683, 1693, 1696, 1698, 1705, 1707, 1710, 1713, 1719, 1723, 1726, 1731, 1739, 1748, 1758, 1768, 1781, 1787, 1789, 1793, 1799, 1800, 1810, 1817, 1823, 1830, 1835, 1839, 1848, 1853, 1859, 1879, 1909, 1929, 1932, 1935, 1961, 1964, 1969, 1979, 1996, 1997, 2002, 2009, 2013, 2015, 2026, 2037, 2056, 2058, 2071, 2074, 2075, 2077, 2080, 2088, 2099, 2104, 2106, 2111, 2133, 2140, 2145, 2147, 2162, 2174, 2175, 2190, 2196, 2204, 2207, 2216, 2219, 2221, 2233, 2234, 2236, 2248, 2251, 2257, 2269, 2273, 2277, 2285, 2286, 2294, 2305, 2309, 2315, 2316, 2319, 2322, 2334, 2339, 2356, 2372, 2378, 2379, 2393, 2403, 2406, 2414, 2418, 2419, 2424, 2425, 2427, 2432, 2434, 2446, 2460, 2467, 2479, 2480, 2482, 2489, 2494, ... |
15 | 2, 3, 11, 17, 23, 43, 46, 52, 53, 61, 62, 78, 84, 88, 89, 92, 99, 108, 123, 124, 141, 146, 154, 156, 158, 163, 170, 171, 182, 187, 202, 217, 219, 221, 229, 233, 238, 248, 249, 253, 264, 274, 275, 278, 283, 285, 287, 291, 296, 302, 309, 314, 315, 322, 325, 342, 346, 353, 356, 366, 368, 372, 377, 380, 384, 394, 404, 406, 411, 420, 425, 426, 446, 461, 463, 466, 470, 480, 482, 486, 487, 488, 494, 495, 498, 499, 508, 518, 521, 533, 540, 552, 554, 573, 580, 592, 593, 594, 595, 612, 624, 633, 636, 644, 647, 672, 681, 703, 707, 711, 712, 718, 719, 721, 724, 737, 740, 756, 760, 766, 791, 792, 801, 811, 821, 832, 852, 864, 872, 905, 914, 915, 938, 942, 946, 983, 984, 985, 990, 996, 1016, 1025, 1038, 1046, 1056, 1070, 1078, 1085, 1116, 1127, 1129, 1143, 1146, 1178, 1179, 1209, 1213, 1217, 1257, 1261, 1265, 1266, 1271, 1283, 1288, 1307, 1331, 1339, 1344, 1360, 1385, 1422, 1434, 1441, 1448, 1451, 1484, 1491, 1499, 1501, 1505, 1509, 1519, 1522, 1549, 1555, 1574, 1575, 1576, 1585, 1587, 1592, 1605, 1 617, 1625, 1639, 1675, 1695, 1698, 1700, 1701, 1705, 1731, 1751, 1753, 1761, 1763, 1772, 1797, 1801, 1834, 1860, 1881, 1893, 1904, 1908, 1923, 1935, 1937, 1938, 1943, 1944, 1956, 1959, 1983, 1985, 2007, 2011, 2014, 2019, 2027, 2032, 2051, 2052, 2061, 2063, 2075, 2078, 2083, 2085, 2106, 2113, 2121, 2123, 2139, 2163, 2168, 2172, 2200, 2206, 2214, 2217, 2226, 2230, 2234, 2248, 2259, 2276, 2278, 2309, 2318, 2326, 2328, 2347, 2357, 2373, 2383, 2388, 2398, 2413, 2440, 2460, 2461, 2473, 2476, 2486, ... |
dieciséis | 2, 4, 9, 13, 33, 43, 47, 51, 53, 69, 81, 118, 132, 140, 145, 152, 185, 205, 208, 237, 239, 240, 242, 288, 290, 305, 306, 323, 341, 365, 373, 378, 392, 395, 409, 426, 433, 434, 442, 451, 455, 491, 501, 508, 510, 519, 531, 540, 542, 553, 557, 562, 565, 577, 596, 610, 664, 680, 682, 705, 723, 732, 747, 782, 795, 800, 808, 835, 841, 859, 866, 876, 884, 892, 916, 918, 934, 951, 956, 973, 990, 1021, 1022, 1028, 1037, 1053, 1054, 1103, 1106, 1113, 1120, 1121, 1135, 1143, 1174, 1199, 1205, 1209, 1211, 1224, 1232, 1239, 1256, 1284, 1307, 1310, 1343, 1351, 1375, 1377, 1379, 1390, 1403, 1446, 1458, 1475, 1477, 1479, 1495, 1505, 1513, 1529, 1531, 1580, 1585, 1602, 1614, 1616, 1623, 1628, 1640, 1681, 1682, 1691, 1698, 1699, 1732, 1749, 1752, 1753, 1755, 1777, 1785, 1800, 1815, 1836, 1837, 1845, 1868, 1871, 1878, 1885, 1930, 1936, 1942, 1947, 1991, 2053, 2061, 2078, 2083, 2090, 2100, 2104, 2117, 2123, 2140, 2159, 2175, 2191, 2193, 2194, 2227, 2257, 2261, 2274, 2279, 2282, 2286, 2291, 2297, 2328, 233 0, 2337, 2359, 2362, 2378, 2405, 2429, 2440, 2467, 2480, 2490, ... |
17 | 2, 11, 18, 20, 21, 28, 31, 55, 57, 62, 84, 87, 97, 107, 109, 129, 147, 149, 157, 160, 170, 181, 188, 189, 191, 205, 207, 241, 247, 251, 274, 295, 297, 315, 327, 335, 349, 351, 355, 358, 364, 365, 368, 379, 383, 410, 419, 423, 431, 436, 438, 466, 472, 506, 513, 527, 557, 571, 597, 599, 614, 637, 653, 656, 688, 708, 709, 720, 740, 762, 835, 836, 874, 974, 976, 980, 982, 986, 987, 1029, 1045, 1054, 1136, 1151, 1171, 1181, 1185, 1208, 1222, 1230, 1236, 1240, 1242, 1280, 1319, 1332, 1367, 1371, 1375, 1392, 1402, 1435, 1447, 1481, 1495, 1496, 1519, 1525, 1530, 1536, 1547, 1556, 1592, 1603, 1607, 1615, 1683, 1692, 1706, 1726, 1775, 1776, 1782, 1793, 1828, 1833, 1846, 1945, 1967, 1988, 1998, 2001, 2002, 2046, 2049, 2064, 2100, 2103, 2108, 2165, 2183, 2192, 2206, 2223, 2249, 2259, 2268, 2295, 2301, 2303, 2312, 2321, 2343, 2351, 2371, 2395, 2406, 2443, 2446, 2466, 2468, 2471, 2492, 2494, ... |
18 | 2, 5, 6, 7, 8, 9, 11, 26, 35, 38, 42, 49, 54, 56, 66, 73, 80, 81, 88, 96, 100, 106, 107, 118, 120, 121, 122, 126, 131, 134, 175, 190, 196, 197, 207, 208, 227, 234, 235, 240, 245, 266, 271, 275, 296, 301, 302, 305, 308, 312, 322, 335, 342, 343, 347, 350, 353, 362, 367, 378, 379, 381, 384, 397, 399, 415, 418, 423, 442, 444, 455, 464, 467, 473, 480, 494, 505, 513, 520, 530, 556, 557, 574, 575, 581, 609, 628, 664, 665, 666, 689, 695, 700, 702, 708, 711, 712, 720, 723, 729, 739, 745, 795, 810, 823, 847, 859, 861, 871, 897, 900, 921, 930, 949, 951, 975, 981, 996, 999, 1034, 1045, 1050, 1072, 1073, 1081, 1089, 1092, 1102, 1108, 1120, 1128, 1132, 1145, 1163, 1165, 1170, 1227, 1235, 1236, 1258, 1265, 1273, 1280, 1291, 1293, 1297, 1301, 1317, 1338, 1339, 1366, 1369, 1377, 1380, 1387, 1391, 1393, 1395, 1403, 1418, 1422, 1450, 1455, 1461, 1469, 1479, 1486, 1494, 1507, 1526, 1527, 1532, 1537, 1544, 1546, 1563, 1566, 1570, 1576, 1596, 1600, 1603, 1605, 1620, 1626, 1627, 1634, 1640, 1662, 1665, 1670, 1671, 1684, 1692, 1721, 1735, 1746, 1747, 1768, 1785, 1798, 1803, 1825, 1830, 1833, 1847, 1850, 1881, 1892, 1899, 1904, 1923, 1938, 1942, 1943, 1944, 1976, 1988, 1994, 2006, 2022, 2045, 2050, 2057, 2059, 2061, 2064, 2071, 2083, 2087, 2120, 2125, 2132, 2145, 2172, 2203, 2221, 2253, 2258, 2269, 2306, 2311, 2325, 2337, 2346, 2373, 2384, 2424, 2440, 2449, 2457, ... |
19 | 2, 10, 11, 12, 14, 19, 24, 40, 45, 46, 48, 65, 66, 67, 75, 85, 90, 103, 105, 117, 119, 137, 147, 164, 167, 179, 181, 205, 220, 235, 242, 253, 254, 263, 268, 277, 303, 315, 332, 337, 366, 369, 370, 389, 399, 404, 424, 431, 446, 449, 480, 481, 506, 509, 521, 523, 531, 547, 567, 573, 581, 622, 646, 651, 673, 736, 761, 768, 787, 797, 807, 810, 811, 817, 840, 846, 857, 867, 869, 870, 888, 899, 902, 951, 971, 988, 990, 992, 1010, 1023, 1027, 1030, 1041, 1042, 1072, 1102, 1112, 1116, 1143, 1147, 1208, 1218, 1223, 1252, 1256, 1257, 1260, 1291, 1330, 1335, 1340, 1402, 1454, 1502, 1536, 1538, 1594, 1622, 1625, 1631, 1642, 1648, 1693, 1701, 1709, 1726, 1734, 1759, 1767, 1779, 1794, 1809, 1822, 1858, 1939, 1954, 1977, 1988, 1992, 1999, 2024, 2030, 2065, 2067, 2081, 2101, 2135, 2150, 2180, 2193, 2196, 2219, 2239, 2293, 2325, 2330, 2336, 2338, 2358, 2382, 2390, 2402, 2403, 2409, 2457, 2461, 2478, 2480, 2499, ... |
20 | 2, 3, 4, 9, 11, 12, 16, 19, 26, 34, 45, 48, 54, 63, 70, 78, 82, 83, 86, 91, 96, 97, 101, 105, 109, 110, 119, 120, 126, 129, 139, 141, 149, 153, 167, 168, 171, 173, 181, 182, 187, 190, 192, 195, 215, 227, 228, 229, 257, 260, 276, 298, 299, 305, 309, 311, 314, 319, 334, 339, 352, 362, 369, 373, 375, 378, 414, 420, 425, 433, 444, 462, 467, 470, 477, 478, 479, 482, 483, 485, 506, 518, 519, 532, 534, 540, 548, 550, 552, 564, 570, 575, 591, 593, 601, 605, 606, 619, 626, 631, 642, 646, 649, 659, 660, 673, 684, 714, 719, 731, 734, 735, 749, 757, 791, 804, 832, 837, 842, 851, 876, 884, 885, 890, 899, 913, 926, 928, 937, 946, 949, 955, 961, 962, 965, 972, 987, 1010, 1044, 1053, 1057, 1085, 1095, 1098, 1104, 1114, 1118, 1125, 1141, 1162, 1170, 1188, 1201, 1207, 1217, 1218, 1220, 1224, 1229, 1234, 1239, 1262, 1294, 1306, 1322, 1327, 1342, 1349, 1362, 1369, 1384, 1394, 1400, 1401, 1423, 1464, 1469, 1475, 1477, 1490, 1491, 1511, 1513, 1521, 1523, 1531, 1534, 1540, 1544, 1567, 1569, 1571, 1585, 1593, 1611, 1617, 1628, 1630, 1631, 1637, 1640, 1641, 1650, 1665, 1672, 1674, 1677, 1699, 1705, 1706, 1710, 1711, 1719, 1721, 1739, 1744, 1763, 1767, 1770, 1794, 1810, 1815, 1817, 1818, 1820, 1844, 1869, 1879, 1886, 1892, 1898, 1902, 1918, 1920, 1930, 1931, 1937, 1942, 1945, 1961, 1964, 1967, 1971, 1978, 1999, 2002, 2016, 2031, 2038, 2043, 2057, 2062, 2068, 2073, 2075, 2079, 2114, 2116, 2117, 2155, 2174, 2185, 2189, 2191, 2205, 2215, 2221, 2226, 2236, 2237, 2239, 2248, 2259, 2269, 2270, 2306, 2307, 2313, 2315, 2338, 2360, 2372, 2377, 2393, 2395, 2409, 2418, 2422, 2429, 2430, 2437, 2474, 2482, 2487, ... |
21 | 2, 3, 6, 7, 12, 18, 22, 27, 28, 30, 35, 41, 59, 63, 69, 72, 112, 116, 127, 128, 132, 133, 136, 140, 156, 164, 166, 172, 191, 198, 202, 215, 218, 219, 247, 276, 288, 305, 307, 323, 334, 343, 377, 383, 433, 474, 479, 516, 519, 521, 532, 534, 538, 549, 575, 586, 613, 622, 646, 647, 675, 680, 688, 692, 733, 737, 790, 793, 795, 815, 822, 902, 909, 911, 915, 947, 952, 966, 996, 1025, 1033, 1034, 1048, 1073, 1075, 1082, 1087, 1093, 1129, 1144, 1163, 1166, 1182, 1188, 1208, 1241, 1251, 1252, 1269, 1274, 1310, 1340, 1363, 1379, 1418, 1424, 1460, 1461, 1463, 1494, 1501, 1503, 1507, 1508, 1510, 1532, 1540, 1553, 1568, 1590, 1595, 1603, 1623, 1627, 1635, 1660, 1682, 1719, 1728, 1749, 1756, 1766, 1790, 1796, 1797, 1826, 1832, 1857, 1879, 1886, 1924, 1929, 1939, 1954, 1974, 1979, 1982, 1983, 1997, 2004, 2012, 2013, 2064, 2075, 2090, 2097, 2099, 2107, 2113, 2118, 2123, 2128, 2134, 2152, 2200, 2205, 2221, 2234, 2243, 2252, 2257, 2262, 2280, 2306, 2320, 2322, 2323, 2376, 2381, 2383, 2410, 2424, 2436, 2 450, 2459, 2480, 2483, ... |
22 | 2, 6, 12, 13, 23, 24, 26, 35, 54, 62, 69, 91, 105, 147, 160, 163, 183, 185, 193, 229, 232, 233, 236, 248, 252, 262, 269, 280, 285, 294, 303, 307, 315, 330, 376, 394, 426, 430, 439, 440, 464, 469, 491, 492, 508, 537, 625, 629, 647, 653, 666, 752, 772, 775, 786, 788, 832, 840, 852, 854, 855, 859, 905, 922, 972, 993, 998, 1012, 1041, 1043, 1061, 1076, 1082, 1129, 1136, 1154, 1158, 1173, 1177, 1199, 1208, 1220, 1237, 1266, 1277, 1312, 1336, 1338, 1370, 1386, 1405, 1429, 1439, 1442, 1451, 1455, 1508, 1522, 1543, 1553, 1564, 1566, 1626, 1665, 1734, 1775, 1810, 1821, 1829, 1840, 1844, 1908, 1910, 1938, 1963, 1982, 2009, 2017, 2040, 2070, 2083, 2101, 2105, 2118, 2155, 2163, 2170, 2201, 2203, 2224, 2231, 2244, 2329, 2346, 2347, 2373, 2433, 2450, 2456, 2461, 2485, 2486, 2493, 2496, ... |
23 | 10, 40, 82, 113, 127, 141, 170, 257, 275, 287, 295, 315, 344, 373, 442, 468, 599, 609, 634, 646, 663, 671, 710, 819, 834, 857, 884, 894, 904, 992, 997, 1060, 1069, 1077, 1120, 1143, 1190, 1232, 1253, 1261, 1280, 1291, 1347, 1407, 1436, 1448, 1483, 1514, 1570, 1642, 1680, 1684, 1691, 1744, 1749, 1786, 1801, 1816, 1830, 1879, 1891, 1906, 1946, 1968, 1994, 2005, 2158, 2200, 2318, 2444, 2459, ... |
24 | 2, 3, 5, 6, 10, 13, 14, 15, 18, 25, 26, 27, 31, 34, 37, 39, 40, 42, 44, 46, 49, 50, 53, 59, 62, 63, 65, 68, 69, 75, 76, 77, 83, 87, 99, 100, 102, 104, 107, 110, 142, 152, 161, 166, 174, 175, 184, 187, 188, 191, 192, 199, 204, 207, 208, 213, 215, 222, 224, 227, 238, 244, 245, 247, 250, 256, 259, 263, 264, 265, 268, 274, 279, 286, 289, 303, 310, 311, 312, 314, 327, 332, 337, 339, 350, 353, 363, 366, 376, 380, 396, 409, 411, 434, 438, 439, 451, 466, 467, 486, 499, 501, 503, 506, 508, 520, 549, 550, 551, 555, 575, 579, 581, 588, 593, 611, 612, 615, 616, 619, 623, 630, 639, 643, 645, 646, 649, 653, 658, 661, 663, 672, 673, 679, 680, 690, 694, 714, 716, 718, 730, 731, 741, 743, 753, 759, 761, 764, 781, 792, 799, 813, 816, 818, 834, 837, 842, 854, 861, 863, 867, 872, 873, 875, 878, 880, 886, 892, 903, 937, 965, 978, 989, 990, 1034, 1036, 1041, 1051, 1055, 1080, 1081, 1082, 1095, 1096, 1104, 1105, 1108, 1122, 1127, 1129, 1133, 1135, 1136, 1148, 1171, 1193, 1217, 1221, 1222, 1241, 1242, 1247, 1 250, 1253, 1254, 1266, 1280, 1281, 1283, 1287, 1292, 1298, 1302, 1308, 1314, 1323, 1330, 1332, 1340, 1355, 1359, 1361, 1373, 1375, 1378, 1379, 1381, 1384, 1389, 1398, 1399, 1411, 1413, 1424, 1445, 1449, 1457, 1461, 1462, 1473, 1483, 1484, 1486, 1487, 1501, 1505, 1521, 1523, 1544, 1557, 1562, 1573, 1583, 1584, 1586, 1590, 1591, 1597, 1610, 1615, 1630, 1638, 1644, 1651, 1652, 1654, 1660, 1664, 1670, 1681, 1688, 1690, 1699, 1704, 1705, 1706, 1707, 1708, 1713, 1715, 1723, 1741, 1743, 1752, 1757, 1767, 1771, 1772, 1775, 1778, 1780, 1797, 1798, 1816, 1822, 1829, 1838, 1848, 1853, 1859, 1869, 1871, 1893, 1904, 1934, 1952, 1957, 1971, 1972, 1973, 1974, 1990, 1998, 2003, 2010, 2011, 2018, 2020, 2022, 2026, 2030, 2031, 2040, 2050, 2070, 2078, 2090, 2094, 2102, 2108, 2115, 2123, 2128, 2129, 2142, 2150, 2156, 2192, 2200, 2208, 2213, 2218, 2238, 2239, 2250, 2264, 2268, 2279, 2295, 2301, 2307, 2310, 2314, 2325, 2334, 2335, 2340, 2346, 2348, 2354, 2364, 2376, 2380, 2381, 2387, 2389, 2393, 2400, 2406, 2407, 2415, 2425, 2427, 2444, 2445, 2453, 2462, 2467, 2474, 2487, ... |
25 | 22, 33, 39, 43, 46, 62, 74, 101, 134, 141, 142, 151, 167, 212, 238, 266, 287, 313, 335, 369, 414, 415, 418, 432, 436, 509, 516, 541, 604, 679, 697, 770, 782, 815, 831, 859, 871, 874, 895, 897, 924, 1039, 1048, 1070, 1085, 1096, 1111, 1121, 1134, 1145, 1170, 1177, 1212, 1239, 1240, 1262, 1321, 1339, 1347, 1361, 1364, 1374, 1407, 1413, 1414, 1449, 1473, 1488, 1513, 1537, 1544, 1624, 1627, 1628, 1630, 1665, 1682, 1691, 1718, 1744, 1758, 1766, 1783, 1792, 1822, 1835, 1979, 2026, 2043, 2046, 2050, 2118, 2159, 2160, 2161, 2165, 2180, 2214, 2223, 2235, 2248, 2250, 2256, 2296, 2308, 2312, 2357, 2368, 2400, 2414, 2433, 2444, 2450, 2487, 2496, ... |
26 | 2, 3, 21, 22, 23, 35, 39, 74, 77, 80, 84, 89, 103, 108, 114, 121, 126, 134, 152, 153, 171, 180, 195, 204, 230, 246, 256, 263, 285, 297, 321, 326, 336, 337, 342, 345, 351, 368, 390, 393, 397, 398, 399, 413, 427, 439, 490, 493, 525, 558, 563, 566, 574, 591, 602, 609, 630, 641, 652, 657, 660, 667, 682, 685, 694, 708, 712, 716, 721, 755, 760, 763, 791, 792, 797, 813, 828, 839, 850, 862, 882, 898, 999, 1025, 1029, 1030, 1035, 1038, 1049, 1063, 1073, 1076, 1081, 1105, 1111, 1128, 1162, 1176, 1178, 1185, 1216, 1227, 1234, 1238, 1264, 1268, 1274, 1307, 1318, 1324, 1359, 1364, 1369, 1371, 1373, 1377, 1388, 1392, 1445, 1450, 1451, 1461, 1489, 1496, 1529, 1539, 1550, 1555, 1560, 1610, 1612, 1616, 1624, 1632, 1689, 1695, 1794, 1805, 1824, 1857, 1873, 1889, 1899, 1930, 1943, 1950, 1955, 1963, 1979, 1985, 1994, 2003, 2005, 2010, 2085, 2103, 2108, 2113, 2122, 2151, 2153, 2172, 2189, 2214, 2228, 2234, 2236, 2257, 2268, 2293, 2307, 2314, 2337, 2373, 2380, 2400, 2417, 2433, 2436, 2443, 2483, 2487, 2492, ... |
27 | 2, 11, 44, 45, 56, 62, 63, 67, 110, 127, 163, 170, 208, 214, 219, 232, 234, 245, 261, 263, 325, 333, 337, 394, 395, 398, 402, 413, 421, 428, 434, 437, 498, 502, 505, 557, 558, 578, 610, 633, 637, 643, 652, 691, 692, 695, 715, 723, 731, 750, 761, 774, 794, 797, 804, 806, 826, 846, 854, 855, 859, 863, 906, 919, 923, 926, 943, 977, 982, 1045, 1046, 1066, 1081, 1085, 1086, 1091, 1094, 1108, 1157, 1164, 1181, 1184, 1197, 1207, 1212, 1217, 1239, 1271, 1282, 1298, 1300, 1303, 1341, 1371, 1378, 1402, 1407, 1458, 1525, 1579, 1596, 1624, 1632, 1679, 1696, 1705, 1725, 1772, 1775, 1804, 1809, 1827, 1828, 1845, 1853, 1867, 1896, 1909, 1912, 1914, 1958, 1960, 1961, 2004, 2005, 2007, 2030, 2061, 2089, 2122, 2131, 2137, 2138, 2145, 2167, 2276, 2316, 2319, 2321, 2322, 2332, 2393, 2394, 2404, 2439, 2458, ... |
28 | 4, 5, 7, 13, 25, 33, 41, 63, 74, 80, 88, 94, 96, 104, 116, 144, 149, 151, 154, 165, 167, 174, 183, 191, 197, 208, 231, 241, 262, 268, 270, 290, 318, 319, 361, 368, 376, 390, 394, 412, 431, 434, 442, 464, 489, 492, 521, 529, 556, 568, 574, 575, 585, 589, 613, 629, 639, 654, 666, 667, 672, 683, 684, 709, 724, 732, 763, 782, 787, 803, 811, 817, 821, 828, 842, 845, 850, 858, 876, 928, 933, 951, 977, 979, 982, 993, 995, 1006, 1020, 1037, 1045, 1056, 1082, 1086, 1089, 1101, 1111, 1135, 1140, 1156, 1166, 1196, 1217, 1218, 1223, 1224, 1246, 1280, 1285, 1306, 1343, 1357, 1368, 1414, 1426, 1428, 1480, 1484, 1509, 1517, 1530, 1536, 1541, 1567, 1571, 1579, 1589, 1594, 1611, 1707, 1712, 1736, 1739, 1744, 1757, 1760, 1763, 1770, 1781, 1791, 1802, 1807, 1818, 1844, 1855, 1862, 1891, 1930, 1942, 1960, 1972, 1985, 1996, 2029, 2043, 2060, 2076, 2170, 2180, 2198, 2213, 2217, 2250, 2261, 2271, 2329, 2340, 2343, 2377, 2412, 2423, 2431, 2464, 2465, 2470, 2482, ... |
29 | 6, 40, 65, 70, 114, 151, 221, 229, 268, 283, 398, 451, 460, 519, 554, 587, 627, 628, 659, 687, 699, 859, 884, 915, 943, 974, 986, 1101, 1120, 1159, 1176, 1212, 1223, 1297, 1312, 1322, 1337, 1390, 1409, 1415, 1446, 1477, 1508, 1592, 1625, 1636, 1683, 1691, 1800, 1802, 1803, 1820, 2020, 2126, 2414, 2421, 2429, 2461, ... |
30 | 2, 6, 7, 8, 9, 16, 18, 20, 26, 29, 31, 32, 33, 40, 41, 47, 57, 76, 82, 87, 88, 93, 101, 109, 120, 121, 125, 133, 140, 144, 162, 163, 175, 178, 183, 186, 191, 196, 215, 216, 218, 227, 233, 242, 253, 266, 267, 273, 276, 278, 304, 312, 317, 319, 328, 336, 374, 380, 391, 408, 413, 421, 436, 438, 439, 448, 453, 457, 474, 475, 479, 491, 500, 502, 505, 510, 511, 521, 526, 541, 558, 560, 564, 609, 621, 625, 628, 636, 648, 657, 660, 678, 682, 683, 692, 705, 712, 714, 727, 738, 746, 759, 767, 782, 783, 802, 803, 826, 831, 833, 836, 837, 844, 846, 851, 863, 882, 898, 924, 925, 931, 938, 946, 953, 970, 975, 976, 984, 988, 990, 1011, 1017, 1054, 1091, 1093, 1115, 1118, 1130, 1142, 1145, 1161, 1162, 1182, 1187, 1201, 1219, 1227, 1250, 1260, 1278, 1281, 1294, 1338, 1356, 1364, 1370, 1379, 1389, 1396, 1397, 1402, 1409, 1420, 1433, 1441, 1451, 1459, 1461, 1467, 1486, 1488, 1489, 1492, 1511, 1517, 1535, 1537, 1555, 1565, 1595, 1610, 1614, 1640, 1643, 1644, 1673, 1704, 1709, 1710, 1715, 1724, 1731, 1732, 1735, 1751, 1776, 1786, 1794, 1797, 1800, 1812, 1824, 1827, 1833, 1836, 1844, 1847, 1848, 1859, 1861, 1862, 1865, 1891, 1892, 1917, 1920, 1929, 1941, 1950, 1951, 1983, 1984, 1994, 2011, 2012, 2033, 2045, 2046, 2056, 2074, 2082, 2097, 2104, 2105, 2108, 2118, 2135, 2148, 2149, 2172, 2178, 2196, 2199, 2202, 2203, 2205, 2206, 2207, 2251, 2258, 2264, 2272, 2278, 2294, 2304, 2332, 2360, 2365, 2385, 2388, 2394, 2403, 2434, 2446, 2463, 2465, 2467, 2472, 2488, 2494, ... |
31 | 2, 14, 19, 31, 44, 53, 71, 82, 117, 127, 131, 145, 156, 177, 197, 203, 241, 258, 261, 276, 283, 293, 320, 325, 373, 379, 387, 388, 406, 413, 461, 462, 470, 486, 491, 534, 549, 569, 582, 612, 618, 639, 696, 706, 723, 746, 765, 767, 774, 796, 802, 877, 878, 903, 923, 931, 981, 991, 998, 1002, 1008, 1049, 1077, 1113, 1114, 1115, 1138, 1146, 1159, 1177, 1189, 1200, 1229, 1270, 1281, 1312, 1359, 1429, 1486, 1493, 1496, 1558, 1605, 1614, 1626, 1632, 1649, 1673, 1698, 1754, 1790, 1859, 1865, 1894, 1900, 1904, 1918, 1939, 1948, 1973, 1998, 1999, 2022, 2031, 2038, 2055, 2111, 2167, 2169, 2180, 2236, 2300, 2377, 2387, 2388, 2422, 2462, 2473, ... |
32 | 2, 3, 9, 29, 41, 44, 73, 74, 76, 81, 87, 94, 111, 113, 156, 157, 158, 167, 173, 176, 187, 188, 195, 198, 199, 248, 253, 288, 295, 301, 306, 309, 318, 330, 348, 370, 371, 382, 391, 396, 403, 435, 441, 452, 456, 470, 474, 476, 478, 485, 525, 560, 568, 575, 585, 589, 598, 599, 607, 617, 642, 657, 669, 686, 688, 690, 736, 774, 776, 778, 779, 789, 790, 830, 832, 834, 846, 900, 905, 916, 946, 955, 956, 969, 972, 982, 984, 995, 1001, 1018, 1023, 1044, 1078, 1083, 1102, 1141, 1147, 1167, 1170, 1176, 1203, 1213, 1214, 1236, 1247, 1252, 1265, 1322, 1349, 1360, 1407, 1408, 1412, 1426, 1457, 1491, 1528, 1535, 1636, 1660, 1674, 1685, 1734, 1747, 1803, 1812, 1822, 1830, 1834, 1835, 1850, 1856, 1860, 1876, 1890, 1891, 1943, 1950, 1979, 1984, 2006, 2027, 2031, 2072, 2078, 2084, 2120, 2135, 2152, 2156, 2159, 2208, 2218, 2230, 2236, 2237, 2271, 2284, 2315, 2318, 2352, 2355, 2377, 2392, 2407, 2415, 2438, 2441, 2448, 2462, ... |
33 | 2, 3, 13, 14, 18, 31, 44, 59, 62, 75, 80, 104, 109, 145, 185, 213, 273, 282, 309, 321, 337, 379, 399, 405, 411, 430, 452, 464, 470, 522, 535, 560, 566, 586, 593, 597, 653, 654, 688, 702, 704, 727, 728, 744, 746, 780, 805, 806, 816, 822, 829, 846, 856, 871, 884, 979, 986, 1001, 1014, 1043, 1087, 1102, 1109, 1133, 1185, 1192, 1211, 1324, 1325, 1340, 1410, 1422, 1474, 1476, 1494, 1503, 1556, 1636, 1648, 1661, 1672, 1716, 1720, 1721, 1723, 1725, 1806, 1810, 1829, 1927, 1975, 1983, 1989, 2085, 2168, 2174, 2189, 2207, 2210, 2275, 2290, 2328, 2331, 2359, 2360, 2369, 2379, 2397, 2419, 2487, ... |
34 | 2, 7, 13, 17, 19, 41, 48, 58, 59, 66, 84, 86, 129, 133, 139, 143, 146, 149, 166, 167, 231, 268, 270, 299, 305, 322, 328, 359, 387, 397, 408, 469, 523, 527, 534, 541, 553, 555, 569, 577, 582, 583, 600, 608, 634, 662, 664, 667, 672, 673, 709, 714, 720, 725, 733, 746, 747, 759, 776, 802, 808, 822, 860, 870, 877, 892, 896, 902, 911, 962, 970, 975, 985, 1034, 1050, 1051, 1070, 1082, 1090, 1109, 1148, 1150, 1168, 1185, 1198, 1200, 1209, 1212, 1233, 1235, 1261, 1281, 1312, 1338, 1339, 1357, 1380, 1382, 1387, 1403, 1411, 1440, 1441, 1459, 1477, 1483, 1497, 1503, 1560, 1561, 1578, 1583, 1689, 1691, 1710, 1751, 1752, 1755, 1789, 1797, 1826, 1883, 1886, 1887, 1901, 1912, 1950, 1955, 1965, 1971, 1986, 2016, 2032, 2038, 2041, 2060, 2071, 2074, 2083, 2093, 2121, 2126, 2139, 2180, 2182, 2193, 2195, 2209, 2247, 2260, 2292, 2294, 2340, 2461, 2493, ... |
35 | 14, 33, 39, 55, 112, 130, 132, 138, 168, 176, 179, 186, 189, 195, 210, 246, 259, 264, 310, 318, 346, 417, 431, 467, 478, 480, 534, 545, 564, 567, 661, 671, 741, 744, 749, 757, 786, 794, 804, 825, 851, 866, 911, 948, 955, 962, 976, 992, 1014, 1033, 1042, 1082, 1109, 1161, 1193, 1220, 1244, 1260, 1268, 1278, 1313, 1414, 1437, 1476, 1563, 1615, 1618, 1658, 1687, 1715, 1738, 1741, 1829, 2016, 2019, 2044, 2045, 2085, 2103, 2105, 2110, 2114, 2118, 2150, 2181, 2198, 2215, 2248, 2260, 2262, 2277, 2286, 2328, 2343, 2366, 2394, 2415, 2440, 2445, 2468, ... |
36 | 3, 7, 9, 10, 11, 14, 27, 30, 33, 37, 40, 51, 62, 71, 78, 80, 82, 95, 117, 125, 137, 142, 148, 157, 185, 189, 191, 197, 223, 232, 236, 252, 255, 265, 287, 321, 323, 324, 326, 332, 337, 341, 354, 369, 391, 414, 416, 418, 430, 487, 509, 545, 558, 563, 582, 588, 589, 618, 675, 694, 714, 715, 739, 773, 776, 788, 884, 898, 909, 928, 932, 935, 948, 950, 952, 969, 989, 996, 1008, 1029, 1040, 1042, 1079, 1085, 1094, 1119, 1124, 1136, 1148, 1159, 1183, 1196, 1207, 1211, 1281, 1296, 1377, 1379, 1380, 1474, 1486, 1516, 1517, 1526, 1538, 1554, 1562, 1563, 1566, 1579, 1582, 1599, 1619, 1628, 1649, 1653, 1655, 1657, 1671, 1773, 1792, 1804, 1809, 1822, 1841, 1849, 1864, 1896, 1912, 1913, 1991, 2012, 2046, 2061, 2071, 2112, 2113, 2115, 2143, 2147, 2160, 2180, 2186, 2211, 2248, 2249, 2263, 2268, 2283, 2302, 2315, 2322, 2347, 2372, 2399, 2426, 2436, 2443, ... |
37 | 61, 77, 94, 97, 99, 113, 126, 130, 134, 147, 161, 172, 187, 202, 208, 246, 261, 273, 285, 302, 320, 432, 444, 503, 523, 525, 563, 666, 680, 709, 740, 757, 787, 902, 962, 964, 969, 1013, 1109, 1111, 1165, 1186, 1219, 1351, 1528, 1587, 1660, 1698, 1710, 1754, 1811, 1972, 2070, 2088, 2137, 2145, 2185, 2210, 2295, 2305, 2348, 2365, 2396, 2398, 2439, 2453, 2462, ... |
38 | 2, 10, 13, 18, 24, 28, 43, 47, 49, 54, 65, 83, 98, 106, 143, 152, 177, 184, 190, 194, 195, 208, 241, 249, 259, 264, 292, 315, 319, 345, 353, 355, 386, 394, 481, 500, 517, 525, 534, 535, 550, 556, 595, 601, 649, 656, 680, 686, 687, 697, 707, 710, 756, 798, 804, 817, 818, 829, 839, 841, 858, 864, 891, 906, 912, 932, 948, 973, 991, 994, 1012, 1030, 1032, 1036, 1046, 1057, 1060, 1066, 1071, 1089, 1166, 1175, 1203, 1205, 1227, 1234, 1237, 1261, 1283, 1284, 1319, 1327, 1335, 1336, 1337, 1356, 1372, 1387, 1412, 1413, 1439, 1450, 1460, 1483, 1488, 1495, 1502, 1515, 1518, 1521, 1532, 1538, 1676, 1677, 1685, 1686, 1690, 1720, 1722, 1734, 1739, 1758, 1759, 1762, 1782, 1792, 1814, 1822, 1833, 1834, 1838, 1839, 1842, 1861, 1869, 1884, 1918, 1922, 1972, 1975, 1999, 2005, 2012, 2033, 2042, 2056, 2093, 2119, 2221, 2244, 2251, 2264, 2325, 2356, 2359, 2371, 2381, 2383, 2427, 2436, 2446, 2479, ... |
39 | 10, 23, 29, 86, 240, 254, 284, 308, 340, 369, 371, 378, 382, 393, 407, 422, 448, 459, 574, 582, 613, 619, 667, 686, 703, 767, 769, 844, 851, 861, 875, 881, 944, 987, 995, 1030, 1056, 1207, 1219, 1233, 1251, 1270, 1279, 1292, 1343, 1372, 1399, 1409, 1445, 1468, 1497, 1500, 1557, 1586, 1598, 1628, 1633, 1645, 1667, 1677, 1712, 1760, 1803, 1807, 1835, 1933, 2004, 2014, 2028, 2039, 2057, 2113, 2136, 2143, 2196, 2224, 2229, 2271, 2291, 2376, 2391, 2397, 2398, ... |
40 | 2, 3, 4, 31, 37, 39, 46, 77, 98, 119, 124, 143, 144, 154, 169, 197, 205, 232, 245, 266, 291, 295, 297, 305, 308, 319, 332, 333, 413, 426, 431, 437, 454, 459, 472, 483, 513, 528, 531, 542, 579, 617, 619, 635, 647, 677, 724, 737, 748, 780, 806, 815, 819, 820, 840, 851, 858, 870, 875, 907, 920, 927, 940, 983, 1002, 1028, 1048, 1050, 1064, 1109, 1125, 1149, 1179, 1197, 1209, 1222, 1229, 1233, 1244, 1248, 1251, 1320, 1337, 1345, 1410, 1434, 1471, 1522, 1526, 1566, 1574, 1576, 1578, 1607, 1723, 1725, 1738, 1758, 1794, 1877, 1885, 1886, 1968, 1999, 2000, 2009, 2010, 2023, 2041, 2058, 2064, 2073, 2093, 2136, 2141, 2148, 2171, 2182, 2183, 2204, 2215, 2222, 2232, 2273, 2275, 2287, 2317, 2323, 2342, 2355, 2364, 2396, 2423, 2428, 2450, 2478, 2487, ... |
41 | 14, 53, 55, 58, 71, 76, 82, 211, 248, 271, 296, 316, 430, 433, 439, 472, 545, 553, 555, 596, 663, 677, 682, 746, 814, 832, 885, 926, 947, 959, 1048, 1121, 1146, 1175, 1207, 1300, 1302, 1390, 1404, 1445, 1466, 1477, 1541, 1650, 1699, 1702, 1706, 1756, 1757, 1782, 1902, 1944, 1963, 1994, 2012, 2042, 2122, 2163, 2215, 2344, 2348, 2369, 2439, 2442, 2465, ... |
42 | 2, 6, 8, 11, 17, 23, 35, 41, 49, 58, 65, 85, 88, 96, 97, 103, 107, 111, 129, 139, 144, 161, 170, 194, 197, 213, 214, 217, 223, 230, 236, 238, 247, 274, 283, 290, 297, 298, 301, 323, 339, 348, 360, 381, 382, 383, 389, 393, 398, 403, 427, 445, 452, 473, 480, 497, 500, 511, 523, 561, 575, 595, 601, 604, 606, 615, 629, 651, 652, 680, 685, 702, 705, 725, 762, 770, 774, 780, 781, 782, 805, 814, 857, 892, 912, 918, 942, 987, 1004, 1027, 1030, 1039, 1045, 1054, 1099, 1125, 1126, 1131, 1155, 1160, 1168, 1169, 1215, 1231, 1235, 1246, 1249, 1256, 1271, 1279, 1289, 1291, 1314, 1315, 1325, 1373, 1383, 1385, 1386, 1415, 1416, 1420, 1436, 1454, 1460, 1468, 1476, 1498, 1519, 1522, 1556, 1585, 1629, 1657, 1665, 1687, 1692, 1693, 1708, 1713, 1715, 1716, 1729, 1730, 1735, 1744, 1779, 1784, 1787, 1794, 1801, 1808, 1810, 1812, 1816, 1842, 1847, 1851, 1857, 1863, 1914, 1924, 1958, 1966, 1974, 1975, 1991, 2001, 2002, 2013, 2022, 2029, 2036, 2052, 2124, 2132, 2138, 2157, 2182, 2207, 2218, 2228, 2229, 2246, 22 51, 2257, 2276, 2279, 2280, 2295, 2303, 2338, 2344, 2360, 2362, 2378, 2387, 2389, 2396, 2406, 2408, 2424, 2465, 2472, 2473, 2486, ... |
43 | 15, 21, 26, 86, 89, 114, 123, 163, 180, 310, 332, 377, 409, 438, 448, 457, 477, 526, 534, 556, 586, 612, 653, 665, 690, 692, 709, 760, 783, 803, 821, 848, 877, 899, 909, 942, 981, 1041, 1042, 1043, 1066, 1068, 1069, 1106, 1126, 1139, 1197, 1310, 1386, 1476, 1561, 1599, 1606, 1636, 1774, 1802, 1835, 1867, 2033, 2068, 2153, 2155, 2229, 2237, 2256, 2269, 2276, 2324, 2467, ... |
44 | 25, 60, 70, 77, 86, 116, 117, 119, 137, 151, 166, 175, 176, 177, 181, 184, 202, 208, 229, 241, 300, 313, 328, 332, 344, 385, 402, 442, 444, 446, 453, 467, 470, 500, 501, 522, 527, 531, 532, 534, 568, 584, 592, 629, 690, 696, 701, 706, 709, 728, 734, 749, 795, 812, 828, 838, 844, 845, 855, 857, 950, 951, 965, 991, 1009, 1011, 1084, 1090, 1098, 1102, 1125, 1142, 1168, 1169, 1170, 1179, 1181, 1191, 1212, 1213, 1234, 1246, 1247, 1262, 1284, 1285, 1304, 1310, 1311, 1358, 1368, 1387, 1411, 1421, 1432, 1459, 1468, 1483, 1485, 1515, 1538, 1542, 1570, 1572, 1587, 1616, 1618, 1628, 1629, 1636, 1646, 1647, 1654, 1662, 1676, 1687, 1710, 1723, 1732, 1734, 1750, 1804, 1807, 1831, 1861, 1865, 1875, 1882, 1899, 1921, 1925, 1942, 1945, 1996, 2014, 2015, 2023, 2036, 2066, 2071, 2078, 2088, 2136, 2149, 2165, 2223, 2232, 2262, 2281, 2287, 2435, 2440, 2462, 2463, 2498, ... |
45 | 11, 18, 23, 24, 29, 33, 40, 51, 61, 65, 85, 91, 95, 113, 153, 206, 207, 218, 264, 276, 285, 292, 313, 332, 347, 362, 367, 391, 417, 418, 424, 426, 428, 439, 444, 451, 454, 468, 476, 493, 542, 601, 634, 642, 653, 657, 680, 705, 734, 764, 783, 787, 856, 867, 873, 915, 942, 945, 953, 964, 971, 1013, 1022, 1044, 1054, 1058, 1070, 1111, 1133, 1152, 1242, 1252, 1274, 1304, 1322, 1334, 1365, 1404, 1405, 1406, 1423, 1438, 1442, 1456, 1483, 1500, 1524, 1527, 1531, 1544, 1553, 1562, 1582, 1662, 1671, 1688, 1723, 1736, 1743, 1751, 1761, 1812, 1830, 1833, 1835, 1837, 1910, 1946, 1985, 1989, 2017, 2022, 2026, 2091, 2095, 2129, 2143, 2166, 2170, 2215, 2271, 2272, 2282, 2283, 2288, 2297, 2300, 2305, 2306, 2308, 2329, 2336, 2364, 2389, 2402, 2416, 2418, 2443, 2448, 2452, 2466, 2472, 2485, 2496, ... |
46 | 2, 3, 7, 16, 17, 18, 25, 46, 47, 106, 110, 111, 118, 136, 144, 145, 230, 238, 361, 382, 422, 439, 474, 494, 495, 519, 588, 639, 657, 707, 733, 751, 802, 831, 863, 902, 925, 976, 994, 1001, 1059, 1140, 1181, 1240, 1249, 1319, 1375, 1442, 1458, 1508, 1699, 1724, 1734, 1751, 1757, 1760, 1766, 1807, 1849, 1897, 1904, 1914, 1922, 1931, 1978, 2029, 2057, 2075, 2139, 2166, 2183, 2209, 2216, 2230, 2241, 2246, 2270, 2307, 2309, 2367, 2429, 2446, 2456, 2460, ... |
47 | 5, 17, 19, 55, 62, 75, 89, 98, 99, 132, 172, 186, 197, 220, 268, 278, 279, 288, 439, 443, 496, 579, 583, 587, 742, 777, 825, 911, 966, 1003, 1029, 1155, 1202, 1267, 1377, 1461, 1472, 1473, 1530, 1562, 1634, 1682, 1705, 1783, 1848, 1852, 1885, 1900, 1943, 1957, 1969, 2036, 2044, 2105, 2111, 2265, 2282, 2485, 2492, ... |
48 | 5, 7, 10, 16, 17, 39, 41, 51, 55, 70, 96, 97, 104, 132, 136, 137, 148, 182, 195, 206, 216, 227, 234, 236, 245, 262, 267, 278, 283, 287, 305, 310, 331, 361, 362, 380, 384, 409, 410, 411, 423, 438, 446, 464, 473, 495, 522, 549, 561, 564, 578, 587, 591, 592, 602, 619, 622, 633, 665, 679, 687, 714, 741, 759, 777, 784, 813, 828, 830, 847, 849, 853, 874, 879, 924, 931, 940, 977, 1015, 1030, 1037, 1057, 1058, 1090, 1107, 1141, 1145, 1160, 1170, 1211, 1246, 1265, 1285, 1296, 1299, 1304, 1306, 1312, 1313, 1316, 1328, 1373, 1393, 1400, 1409, 1420, 1443, 1500, 1518, 1542, 1546, 1557, 1570, 1574, 1643, 1644, 1653, 1656, 1685, 1686, 1688, 1727, 1737, 1756, 1759, 1761, 1762, 1763, 1780, 1792, 1807, 1900, 1924, 1927, 1930, 1936, 1959, 1964, 1977, 2015, 2018, 2019, 2033, 2041, 2050, 2059, 2070, 2089, 2122, 2133, 2179, 2208, 2217, 2222, 2255, 2302, 2313, 2318, 2342, 2350, 2384, 2407, 2416, 2417, 2430, 2440, 2443, 2470, 2477, 2487, ... |
49 | 2, 5, 50, 57, 62, 67, 104, 123, 138, 151, 155, 186, 194, 233, 236, 253, 261, 269, 306, 337, 359, 416, 425, 439, 557, 613, 695, 705, 742, 748, 757, 821, 832, 884, 885, 892, 897, 902, 936, 937, 988, 1125, 1165, 1176, 1248, 1265, 1320, 1337, 1386, 1401, 1544, 1590, 1594, 1675, 1707, 1712, 1714, 1722, 1725, 1798, 1840, 1844, 2037, 2106, 2117, 2148, 2153, 2154, 2155, 2175, 2192, 2208, 2235, 2286, 2292, 2376, 2384, 2416, 2422, 2470, ... |
50 | 6, 7, 17, 29, 42, 44, 56, 59, 62, 106, 108, 112, 141, 161, 163, 173, 194, 210, 212, 229, 231, 254, 296, 306, 342, 360, 382, 384, 395, 400, 416, 418, 431, 435, 457, 458, 484, 492, 517, 519, 530, 531, 540, 551, 579, 609, 618, 637, 644, 672, 697, 713, 722, 724, 732, 790, 791, 794, 810, 839, 850, 852, 876, 898, 902, 914, 926, 928, 937, 938, 970, 1010, 1091, 1118, 1123, 1129, 1150, 1157, 1165, 1182, 1214, 1229, 1247, 1253, 1258, 1269, 1272, 1320, 1321, 1378, 1399, 1402, 1422, 1425, 1474, 1500, 1532, 1539, 1573, 1578, 1584, 1586, 1588, 1622, 1624, 1635, 1651, 1653, 1696, 1699, 1725, 1756, 1811, 1875, 1912, 1948, 1970, 2017, 2076, 2092, 2114, 2115, 2119, 2124, 2131, 2133, 2147, 2175, 2219, 2253, 2260, 2295, 2347, 2406, 2462, 2463, 2464, ... |
51 | 30, 39, 42, 56, 73, 99, 114, 142, 193, 214, 263, 268, 320, 329, 381, 397, 432, 435, 446, 476, 477, 499, 538, 580, 584, 585, 652, 685, 689, 837, 845, 867, 954, 1040, 1108, 1160, 1164, 1283, 1302, 1441, 1450, 1456, 1469, 1609, 1645, 1718, 1720, 1759, 2004, 2065, 2068, 2206, 2289, 2332, 2377, 2383, 2416, 2438, 2443, 2458, ... |
52 | 11, 16, 37, 70, 96, 121, 131, 187, 280, 281, 317, 396, 441, 501, 554, 582, 696, 704, 733, 735, 765, 831, 876, 891, 894, 967, 1013, 1014, 1049, 1071, 1085, 1096, 1119, 1129, 1151, 1162, 1170, 1281, 1289, 1435, 1544, 1594, 1597, 1620, 1653, 1697, 1738, 1740, 1774, 1831, 1864, 1893, 1895, 1899, 1924, 1931, 1944, 1948, 1955, 1977, 2007, 2014, 2021, 2083, 2084, 2186, 2215, 2216, 2268, 2283, 2375, 2422, 2461, ... |
53 | 24, 45, 60, 165, 235, 272, 285, 298, 307, 381, 416, 429, 623, 799, 858, 924, 929, 936, 1034, 1067, 1076, 1130, 1223, 1243, 1327, 1488, 1592, 1594, 1659, 1673, 1676, 1678, 1762, 1873, 1917, 1928, 1997, 2110, 2117, 2141, 2166, 2231, 2243, 2293, 2338, 2380, 2420, 2424, 2428, 2463, 2466, ... |
54 | 2, 7, 9, 15, 23, 24, 25, 42, 62, 63, 78, 91, 122, 151, 159, 201, 208, 222, 248, 252, 277, 281, 284, 286, 291, 299, 316, 340, 342, 378, 395, 440, 445, 460, 478, 498, 522, 528, 532, 558, 580, 600, 668, 688, 701, 710, 726, 743, 752, 757, 763, 766, 771, 778, 787, 796, 798, 805, 812, 856, 864, 882, 893, 895, 963, 981, 987, 992, 1014, 1031, 1046, 1061, 1088, 1098, 1108, 1128, 1163, 1170, 1182, 1191, 1201, 1234, 1266, 1269, 1343, 1373, 1383, 1386, 1460, 1467, 1487, 1508, 1535, 1544, 1575, 1588, 1598, 1650, 1662, 1668, 1697, 1717, 1730, 1738, 1750, 1762, 1766, 1795, 1847, 1852, 1869, 1878, 1894, 1905, 1910, 1912, 1925, 1932, 1952, 1963, 1996, 2015, 2018, 2021, 2105, 2108, 2122, 2141, 2161, 2170, 2188, 2194, 2203, 2235, 2238, 2245, 2251, 2266, 2335, 2366, 2379, 2403, 2431, 2496, ... |
55 | 7, 14, 39, 53, 61, 83, 127, 148, 154, 199, 208, 228, 249, 281, 288, 340, 430, 435, 476, 511, 525, 533, 534, 541, 594, 663, 668, 670, 671, 678, 683, 728, 739, 821, 830, 865, 867, 871, 873, 891, 922, 982, 992, 1037, 1038, 1059, 1090, 1206, 1212, 1252, 1311, 1413, 1443, 1456, 1522, 1537, 1544, 1575, 1616, 1639, 1651, 1668, 1699, 1735, 1741, 1742, 1754, 1756, 1790, 1806, 1820, 1821, 1823, 1958, 2005, 2058, 2064, 2149, 2167, 2169, 2188, 2194, 2226, 2291, 2316, ... |
56 | 2, 5, 12, 19, 23, 33, 34, 84, 130, 136, 159, 167, 183, 187, 192, 197, 226, 229, 253, 259, 260, 269, 274, 323, 332, 337, 381, 404, 444, 464, 487, 491, 496, 520, 527, 577, 583, 614, 666, 672, 678, 683, 688, 702, 742, 747, 748, 762, 790, 830, 857, 865, 869, 871, 898, 901, 946, 1016, 1163, 1245, 1273, 1275, 1280, 1361, 1362, 1371, 1386, 1410, 1457, 1473, 1476, 1488, 1515, 1537, 1559, 1563, 1567, 1570, 1574, 1581, 1600, 1614, 1647, 1689, 1699, 1725, 1769, 1787, 1796, 1804, 1809, 1811, 1837, 1861, 1883, 1888, 1917, 1940, 1964, 1986, 2006, 2027, 2039, 2053, 2137, 2141, 2155, 2179, 2200, 2221, 2227, 2232, 2241, 2318, 2339, 2341, 2345, 2359, 2377, 2389, 2391, 2396, 2401, ... |
57 | 5, 42, 45, 54, 95, 125, 145, 147, 166, 211, 250, 274, 338, 407, 445, 522, 619, 621, 636, 648, 649, 657, 691, 733, 745, 775, 808, 878, 903, 920, 946, 1040, 1064, 1097, 1105, 1122, 1137, 1167, 1168, 1188, 1190, 1197, 1209, 1210, 1211, 1269, 1280, 1319, 1374, 1443, 1477, 1491, 1514, 1520, 1553, 1565, 1586, 1592, 1596, 1624, 1630, 1639, 1656, 1667, 1703, 1769, 1775, 1778, 1790, 1824, 1900, 1918, 1925, 1935, 1939, 1952, 1996, 2023, 2076, 2151, 2168, 2201, 2258, 2294, 2325, 2331, 2333, 2353, 2369, 2407, 2460, 2487, ... |
58 | 7, 15, 25, 62, 119, 123, 154, 202, 245, 285, 294, 295, 357, 371, 476, 626, 664, 690, 708, 723, 737, 768, 783, 803, 825, 826, 835, 841, 842, 867, 871, 897, 904, 934, 953, 1066, 1069, 1088, 1097, 1108, 1183, 1197, 1202, 1259, 1302, 1364, 1461, 1478, 1497, 1528, 1559, 1638, 1715, 1760, 1764, 1815, 1821, 1849, 1854, 1874, 2047, 2086, 2091, 2100, 2133, 2160, 2231, 2242, 2316, 2422, ... |
59 | 19, 70, 102, 116, 126, 188, 209, 257, 294, 359, 451, 461, 468, 470, 638, 653, 710, 762, 766, 781, 824, 901, 939, 964, 995, 1036, 1047, 1098, 1150, 1211, 1234, 1243, 1256, 1278, 1389, 1401, 1422, 1436, 1454, 1492, 1523, 1639, 1703, 1705, 1826, 1913, 1915, 1978, 2013, 2043, 2131, 2140, 2200, 2208, 2228, 2229, 2307, 2309, 2323, 2365, 2480, 2485, ... |
60 | 3, 4, 11, 12, 14, 25, 48, 57, 62, 70, 84, 93, 100, 126, 135, 138, 167, 170, 171, 184, 186, 194, 198, 205, 212, 217, 220, 222, 239, 240, 285, 292, 300, 318, 321, 339, 361, 378, 390, 391, 404, 419, 461, 500, 501, 509, 526, 546, 574, 606, 622, 635, 670, 671, 675, 717, 721, 723, 744, 747, 778, 789, 802, 804, 809, 822, 832, 903, 919, 929, 937, 965, 1001, 1012, 1016, 1024, 1034, 1050, 1084, 1086, 1095, 1101, 1132, 1158, 1164, 1174, 1187, 1211, 1215, 1217, 1223, 1262, 1266, 1276, 1282, 1303, 1320, 1342, 1343, 1346, 1365, 1394, 1395, 1403, 1425, 1430, 1450, 1485, 1502, 1504, 1505, 1506, 1624, 1676, 1705, 1711, 1719, 1722, 1741, 1747, 1748, 1750, 1753, 1766, 1797, 1806, 1859, 1870, 1882, 1900, 1912, 1913, 1916, 1925, 1994, 2001, 2004, 2027, 2041, 2085, 2090, 2095, 2107, 2116, 2122, 2126, 2144, 2169, 2177, 2185, 2188, 2199, 2306, 2317, 2331, 2334, 2341, 2366, 2379, 2394, 2406, 2411, 2426, 2429, 2437, 2486, 2488, 2490, 2498, ... |
61 | 2, 19, 69, 88, 138, 155, 205, 234, 306, 336, 420, 425, 455, 470, 525, 555, 561, 608, 626, 667, 674, 766, 779, 846, 851, 937, 971, 998, 1053, 1055, 1112, 1137, 1263, 1329, 1383, 1445, 1448, 1499, 1544, 1551, 1578, 1640, 1689, 1724, 1750, 1793, 1868, 1892, 2143, 2241, 2358, 2407, 2414, 2441, ... |
62 | 2, 6, 10, 36, 65, 74, 78, 83, 106, 115, 120, 148, 154, 161, 163, 168, 176, 189, 194, 197, 266, 270, 288, 331, 385, 399, 407, 410, 412, 413, 431, 468, 513, 524, 546, 569, 572, 578, 581, 600, 611, 619, 625, 626, 647, 719, 723, 756, 832, 834, 849, 922, 986, 1006, 1007, 1047, 1064, 1102, 1199, 1217, 1247, 1332, 1335, 1349, 1353, 1372, 1374, 1382, 1400, 1405, 1410, 1418, 1419, 1422, 1426, 1444, 1456, 1457, 1554, 1568, 1590, 1622, 1678, 1680, 1683, 1684, 1695, 1725, 1797, 1840, 1847, 1861, 1874, 1895, 1939, 1950, 1987, 1988, 1990, 1999, 2070, 2081, 2093, 2180, 2183, 2212, 2216, 2220, 2227, 2266, 2303, 2337, 2349, 2389, 2408, 2418, 2426, ... |
63 | 3, 7, 12, 40, 92, 122, 178, 191, 195, 214, 282, 283, 297, 299, 300, 418, 437, 467, 493, 497, 507, 512, 530, 597, 630, 664, 667, 701, 744, 800, 823, 876, 899, 944, 965, 1040, 1043, 1061, 1063, 1070, 1083, 1112, 1141, 1209, 1254, 1322, 1325, 1345, 1378, 1398, 1416, 1430, 1532, 1563, 1625, 1704, 1726, 1728, 1746, 1863, 1875, 1921, 1997, 2030, 2085, 2179, 2220, 2319, 2392, 2461, 2476, ... |
64 | 3, 9, 21, 30, 54, 65, 75, 96, 112, 114, 132, 156, 163, 181, 191, 229, 251, 332, 342, 360, 363, 376, 428, 430, 432, 448, 527, 562, 583, 588, 589, 605, 726, 738, 763, 804, 831, 839, 847, 850, 884, 971, 1068, 1099, 1127, 1142, 1167, 1181, 1198, 1199, 1201, 1225, 1243, 1255, 1273, 1299, 1306, 1315, 1379, 1489, 1540, 1547, 1568, 1596, 1673, 1678, 1713, 1714, 1754, 1801, 1812, 1818, 1823, 1847, 1861, 1878, 1906, 1957, 1960, 1962, 1987, 2046, 2069, 2087, 2098, 2109, 2118, 2142, 2177, 2195, 2325, 2330, 2385, 2418, 2434, 2457, ... |
sesenta y cinco | 2, 68, 71, 83, 87, 92, 132, 137, 316, 390, 394, 407, 451, 534, 553, 587, 597, 622, 652, 733, 735, 771, 781, 846, 871, 879, 892, 901, 943, 987, 1047, 1077, 1102, 1120, 1179, 1208, 1219, 1224, 1229, 1261, 1303, 1371, 1614, 1623, 1648, 1726, 1745, 1796, 1810, 1813, 1821, 1842, 1920, 1965, 2147, 2153, 2156, 2193, 2330, 2434, ... |
66 | 9, 38, 40, 53, 62, 105, 107, 125, 129, 134, 156, 183, 193, 210, 276, 283, 294, 306, 307, 317, 345, 371, 388, 399, 447, 504, 508, 514, 529, 542, 585, 594, 648, 668, 671, 676, 717, 719, 722, 723, 743, 752, 772, 784, 818, 833, 840, 844, 870, 880, 896, 941, 942, 964, 978, 1021, 1087, 1115, 1144, 1168, 1182, 1194, 1212, 1215, 1239, 1366, 1378, 1527, 1532, 1562, 1603, 1630, 1644, 1712, 1718, 1780, 1831, 1851, 1864, 1881, 1882, 1885, 1890, 1929, 1941, 1943, 1949, 1957, 1980, 2003, 2036, 2052, 2110, 2124, 2158, 2226, 2269, 2317, 2331, 2344, 2366, 2388, 2422, 2452, ... |
67 | 46, 122, 238, 304, 314, 315, 328, 332, 346, 372, 382, 426, 440, 491, 496, 510, 524, 528, 566, 638, 733, 826, 1016, 1054, 1071, 1214, 1309, 1338, 1388, 1401, 1457, 1512, 1536, 1582, 1624, 1718, 1773, 1814, 1816, 1825, 1952, 1985, 2021, 2072, 2308, 2349, 2449, 2481, ... |
68 | 47, 85, 88, 94, 150, 175, 177, 190, 194, 197, 203, 210, 217, 233, 254, 259, 315, 316, 322, 345, 371, 405, 451, 500, 505, 510, 562, 572, 619, 658, 730, 759, 838, 889, 926, 959, 983, 1041, 1090, 1110, 1136, 1145, 1218, 1249, 1251, 1336, 1373, 1374, 1376, 1392, 1416, 1418, 1425, 1484, 1513, 1547, 1562, 1567, 1581, 1590, 1641, 1657, 1804, 1824, 1829, 1903, 1949, 1952, 1966, 1971, 1990, 2001, 2028, 2031, 2059, 2095, 2109, 2119, 2277, 2372, 2381, 2416, 2421, ... |
69 | 2, 22, 26, 43, 82, 218, 271, 273, 386, 392, 412, 469, 589, 599, 616, 686, 689, 807, 842, 848, 855, 867, 1055, 1138, 1170, 1251, 1287, 1352, 1393, 1422, 1555, 1590, 1617, 1662, 1712, 1745, 1851, 1998, 1999, 2069, 2076, 2189, 2213, 2279, 2328, 2440, ... |
70 | 3, 12, 16, 19, 24, 37, 50, 57, 110, 148, 166, 169, 174, 181, 192, 212, 228, 233, 242, 330, 370, 380, 469, 492, 505, 514, 576, 583, 655, 657, 676, 678, 716, 726, 734, 776, 786, 829, 857, 994, 1040, 1099, 1114, 1154, 1181, 1186, 1244, 1338, 1348, 1350, 1354, 1379, 1397, 1436, 1444, 1509, 1517, 1549, 1557, 1591, 1645, 1741, 1752, 1755, 1801, 1813, 1855, 1900, 1925, 1935, 1949, 1960, 1971, 2003, 2004, 2069, 2082, 2084, 2089, 2113, 2130, 2167, 2259, 2286, 2288, 2301, 2338, 2361, 2362, 2380, 2382, 2386, 2393, 2401, 2420, ... |
71 | 3, 6, 17, 24, 37, 89, 132, 374, 387, 402, 421, 435, 453, 464, 490, 516, 708, 736, 919, 947, 981, 1033, 1067, 1170, 1195, 1253, 1284, 1349, 1385, 1409, 1479, 1709, 1724, 1726, 1735, 1875, 1950, 1984, 2012, 2070, 2124, 2133, 2161, 2194, 2202, 2424, 2432, 2459, ... |
72 | 3, 18, 36, 43, 51, 77, 89, 150, 178, 195, 209, 219, 244, 254, 265, 280, 290, 294, 314, 322, 340, 341, 362, 363, 371, 377, 386, 416, 450, 474, 488, 494, 511, 546, 548, 554, 576, 611, 625, 647, 723, 740, 760, 766, 800, 801, 803, 807, 820, 827, 835, 883, 940, 943, 956, 976, 1013, 1041, 1105, 1161, 1193, 1198, 1217, 1257, 1321, 1333, 1379, 1380, 1405, 1430, 1472, 1550, 1555, 1568, 1698, 1729, 1736, 1750, 1828, 1829, 1841, 1844, 1950, 1952, 1954, 1994, 1998, 2060, 2074, 2123, 2129, 2160, 2174, 2225, 2233, 2244, 2284, 2286, 2392, 2401, 2407, 2411, 2417, 2428, 2473, 2488, ... |
73 | 11, 15, 75, 114, 195, 215, 295, 335, 378, 559, 566, 650, 660, 832, 871, 904, 966, 1021, 1112, 1203, 1334, 1433, 1485, 1724, 1822, 1959, 1998, 2115, 2154, 2432, 2465, 2486, ... |
74 | 16, 19, 21, 49, 56, 63, 71, 74, 77, 83, 92, 96, 99, 160, 172, 197, 198, 230, 241, 280, 283, 415, 425, 448, 490, 520, 627, 691, 735, 784, 803, 829, 842, 853, 871, 872, 893, 894, 973, 981, 989, 1043, 1060, 1061, 1071, 1179, 1182, 1203, 1290, 1299, 1317, 1370, 1389, 1477, 1478, 1496, 1562, 1601, 1624, 1714, 1789, 1848, 1890, 1942, 2016, 2083, 2156, 2217, 2250, 2253, 2266, 2313, 2315, 2319, 2323, 2343, 2358, 2361, 2363, 2383, 2396, 2398, 2399, 2401, 2486, ... |
75 | 59, 73, 75, 165, 181, 204, 205, 208, 283, 369, 377, 396, 427, 448, 531, 535, 573, 587, 601, 628, 664, 686, 705, 727, 836, 860, 866, 879, 907, 918, 1077, 1118, 1142, 1175, 1220, 1256, 1284, 1332, 1337, 1349, 1389, 1412, 1426, 1437, 1453, 1493, 1499, 1502, 1551, 1561, 1640, 1737, 1748, 1789, 1796, 1958, 1975, 2056, 2089, 2090, 2143, 2158, 2177, 2210, 2212, 2245, 2300, 2306, 2347, 2371, 2415, 2424, 2491, ... |
76 | 7, 29, 33, 39, 62, 69, 81, 82, 139, 165, 180, 185, 196, 253, 273, 274, 278, 337, 348, 358, 376, 389, 412, 419, 439, 507, 521, 533, 555, 571, 600, 605, 611, 621, 623, 626, 650, 658, 701, 714, 727, 733, 758, 767, 795, 817, 866, 868, 869, 878, 881, 885, 896, 905, 932, 949, 983, 1013, 1045, 1072, 1082, 1128, 1144, 1162, 1170, 1171, 1196, 1258, 1276, 1285, 1294, 1307, 1315, 1355, 1416, 1423, 1424, 1430, 1442, 1495, 1532, 1535, 1557, 1615, 1651, 1659, 1664, 1669, 1764, 1816, 1833, 1852, 1872, 1930, 1931, 1965, 2077, 2103, 2104, 2182, 2211, 2235, 2271, 2333, 2341, 2402, 2427, 2480, 2481, ... |
77 | 2, 17, 41, 42, 90, 104, 130, 132, 186, 211, 224, 228, 235, 259, 307, 319, 362, 410, 412, 537, 603, 605, 783, 789, 795, 811, 814, 854, 858, 861, 877, 892, 906, 940, 1003, 1028, 1052, 1095, 1178, 1241, 1249, 1259, 1263, 1265, 1279, 1357, 1392, 1398, 1457, 1569, 1755, 1795, 1809, 1814, 1880, 1882, 1894, 1896, 1906, 1961, 1970, 2020, 2026, 2054, 2132, 2161, 2179, 2253, 2310, 2327, 2408, 2451, ... |
78 | 2, 8, 13, 16, 18, 41, 87, 88, 123, 134, 137, 141, 166, 180, 198, 236, 270, 288, 293, 299, 321, 361, 405, 416, 422, 450, 457, 492, 495, 514, 558, 580, 602, 605, 673, 697, 712, 713, 724, 743, 784, 805, 879, 884, 893, 1013, 1017, 1049, 1067, 1094, 1117, 1157, 1212, 1231, 1272, 1306, 1331, 1437, 1447, 1462, 1493, 1528, 1542, 1570, 1572, 1589, 1624, 1676, 1726, 1809, 1818, 1819, 1830, 1843, 1900, 1904, 1929, 1965, 1998, 2000, 2027, 2031, 2065, 2133, 2152, 2159, 2206, 2252, 2374, 2414, 2425, 2448, 2449, 2451, 2462, 2471, 2499, ... |
79 | 22, 112, 140, 158, 159, 170, 254, 271, 330, 334, 354, 390, 483, 528, 560, 565, 714, 850, 888, 924, 929, 933, 935, 970, 1019, 1047, 1141, 1265, 1266, 1338, 1359, 1376, 1412, 1485, 1504, 1542, 1598, 1607, 1618, 1747, 1773, 1814, 1843, 2055, 2087, 2088, 2100, 2167, 2186, 2233, 2311, 2358, 2359, 2363, 2429, ... |
80 | 2, 12, 13, 53, 71, 97, 123, 149, 150, 172, 197, 202, 228, 252, 286, 310, 323, 331, 335, 338, 367, 378, 400, 401, 404, 488, 504, 550, 569, 589, 615, 657, 673, 681, 699, 722, 770, 779, 787, 795, 857, 995, 1002, 1004, 1006, 1008, 1054, 1063, 1115, 1129, 1138, 1183, 1187, 1196, 1200, 1201, 1227, 1235, 1266, 1272, 1295, 1314, 1342, 1383, 1402, 1407, 1416, 1421, 1435, 1439, 1461, 1476, 1480, 1510, 1514, 1525, 1554, 1568, 1596, 1620, 1626, 1640, 1658, 1686, 1695, 1719, 1763, 1894, 1942, 2008, 2020, 2051, 2060, 2132, 2139, 2144, 2183, 2199, 2220, 2244, 2246, 2263, 2397, 2468, 2471, ... |
81 | 21, 28, 50, 77, 79, 142, 153, 191, 194, 310, 311, 405, 440, 462, 557, 562, 638, 659, 690, 724, 746, 852, 868, 887, 919, 922, 944, 945, 1140, 1183, 1326, 1344, 1452, 1463, 1486, 1507, 1579, 1607, 1632, 1652, 1659, 1683, 1710, 1788, 1801, 1812, 1851, 1891, 1925, 1943, 1992, 2157, 2294, 2309, 2352, 2402, 2473, ... |
82 | 61, 63, 99, 144, 230, 312, 360, 401, 413, 424, 451, 515, 542, 567, 610, 618, 622, 651, 690, 732, 817, 871, 1007, 1100, 1106, 1156, 1278, 1403, 1427, 1460, 1535, 1557, 1572, 1604, 1681, 1742, 1802, 1820, 1847, 1903, 1910, 1913, 1978, 2019, 2104, 2134, 2152, 2169, 2309, 2383, 2491, ... |
83 | 41, 146, 386, 593, 667, 688, 906, 927, 930, 1025, 1032, 1111, 1410, 1437, 1638, 1829, 1960, 2045, 2159, 2381, 2384, ... |
84 | 7, 12, 53, 61, 70, 71, 91, 132, 142, 156, 165, 166, 173, 187, 209, 218, 219, 236, 244, 260, 266, 270, 276, 286, 287, 306, 315, 324, 351, 361, 400, 424, 452, 461, 501, 502, 549, 569, 613, 615, 630, 631, 632, 639, 659, 669, 698, 710, 718, 721, 728, 751, 757, 782, 794, 797, 798, 826, 828, 831, 851, 853, 878, 883, 893, 895, 915, 919, 947, 965, 981, 984, 986, 1055, 1078, 1119, 1160, 1175, 1183, 1186, 1188, 1206, 1260, 1267, 1280, 1308, 1310, 1326, 1329, 1341, 1342, 1364, 1401, 1419, 1436, 1438, 1473, 1488, 1506, 1510, 1539, 1550, 1593, 1612, 1630, 1653, 1659, 1663, 1684, 1687, 1705, 1708, 1746, 1754, 1765, 1766, 1768, 1770, 1777, 1839, 1884, 1911, 1918, 1967, 1984, 1987, 1990, 2011, 2045, 2050, 2061, 2084, 2103, 2123, 2156, 2177, 2181, 2229, 2240, 2245, 2246, 2250, 2256, 2259, 2265, 2269, 2291, 2307, 2309, 2310, 2349, 2358, 2376, 2391, 2392, 2427, 2481, 2491, 2492, ... |
85 | 2, 15, 32, 65, 77, 116, 154, 173, 197, 233, 250, 267, 392, 430, 453, 516, 558, 740, 791, 826, 844, 860, 861, 867, 868, 963, 1009, 1010, 1048, 1055, 1097, 1198, 1200, 1220, 1243, 1290, 1329, 1434, 1619, 1621, 1623, 1652, 1710, 1743, 1745, 1827, 1836, 1880, 1932, 2059, 2091, 2109, 2196, ... |
86 | 2, 3, 6, 22, 59, 83, 91, 95, 120, 148, 195, 196, 201, 247, 252, 257, 264, 315, 360, 378, 458, 555, 680, 792, 893, 1025, 1088, 1158, 1171, 1240, 1280, 1416, 1437, 1632, 1661, 1677, 1681, 1849, 1946, 1960, 2007, 2090, 2092, 2225, 2242, 2244, 2377, 2483, ... |
87 | 8, 27, 33, 34, 59, 118, 119, 124, 155, 189, 249, 263, 270, 275, 286, 334, 342, 382, 402, 414, 421, 468, 474, 486, 501, 530, 563, 577, 655, 697, 764, 895, 915, 932, 1108, 1175, 1188, 1228, 1234, 1268, 1277, 1308, 1357, 1358, 1370, 1373, 1400, 1491, 1519, 1529, 1558, 1560, 1658, 1693, 1699, 1735, 1745, 1773, 1805, 1866, 1876, 1905, 1915, 1961, 1996, 2161, 2192, 2227, 2297, 2321, 2446, 2483, ... |
88 | 5, 97, 131, 189, 199, 200, 258, 263, 289, 317, 352, 398, 470, 533, 554, 601, 603, 606, 732, 764, 765, 819, 869, 872, 888, 961, 1197, 1299, 1355, 1435, 1469, 1471, 1522, 1577, 1582, 1638, 1649, 1743, 1768, 1788, 1829, 1860, 1879, 1946, 1994, 2091, 2208, 2289, 2297, 2302, 2322, 2378, 2401, 2475, 2487, ... |
89 | 2, 114, 159, 190, 234, 251, 436, 616, 834, 878, 1008, 1049, 1060, 1062, 1118, 1472, 1689, 1792, 2282, 2334, 2463, 2494, ... |
90 | 2, 5, 6, 58, 66, 71, 78, 80, 96, 101, 122, 127, 148, 153, 183, 194, 198, 211, 244, 258, 261, 354, 387, 390, 413, 415, 446, 447, 450, 465, 475, 480, 502, 524, 532, 549, 577, 590, 607, 608, 610, 620, 623, 635, 668, 678, 716, 793, 844, 859, 862, 879, 895, 915, 958, 963, 969, 974, 1009, 1035, 1080, 1093, 1095, 1136, 1137, 1178, 1219, 1225, 1230, 1296, 1301, 1309, 1315, 1352, 1359, 1369, 1375, 1381, 1383, 1389, 1411, 1450, 1453, 1463, 1514, 1599, 1638, 1651, 1682, 1692, 1705, 1710, 1734, 1768, 1803, 1850, 1883, 1936, 1965, 2037, 2041, 2066, 2108, 2111, 2114, 2117, 2120, 2145, 2164, 2195, 2210, 2225, 2287, 2293, 2327, 2382, 2387, 2389, 2406, 2407, 2458, 2470, 2472, 2483, 2485, 2498, ... |
91 | 11, 19, 28, 30, 46, 80, 116, 140, 159, 198, 272, 331, 357, 360, 448, 544, 728, 827, 854, 910, 937, 1019, 1041, 1106, 1164, 1174, 1226, 1229, 1287, 1307, 1327, 1348, 1408, 1471, 1473, 1618, 1642, 1751, 1810, 1900, 1965, 1976, 2051, 2110, 2206, 2226, 2254, 2331, ... |
92 | 4, 5, 12, 19, 43, 47, 70, 164, 183, 225, 258, 261, 287, 297, 306, 323, 335, 340, 351, 363, 383, 397, 442, 534, 545, 558, 572, 594, 624, 652, 656, 659, 666, 673, 681, 696, 701, 724, 730, 773, 810, 887, 923, 933, 972, 997, 1002, 1006, 1061, 1124, 1135, 1178, 1196, 1225, 1230, 1313, 1356, 1407, 1409, 1451, 1452, 1483, 1576, 1586, 1602, 1607, 1612, 1619, 1667, 1691, 1697, 1823, 1827, 1935, 1963, 1992, 2035, 2099, 2138, 2156, 2199, 2252, 2274, 2299, 2393, 2398, 2447, 2477, ... |
93 | 2, 10, 15, 22, 27, 63, 98, 113, 142, 156, 188, 236, 278, 282, 293, 300, 315, 333, 353, 374, 420, 487, 509, 558, 580, 592, 793, 924, 1099, 1131, 1195, 1242, 1268, 1274, 1321, 1357, 1413, 1484, 1542, 1547, 1611, 1683, 1699, 1702, 1711, 1730, 1746, 1760, 1819, 1854, 1895, 1902, 2026, 2077, 2092, 2111, 2151, 2222, 2272, 2328, 2388, 2390, 2409, 2450, 2475, 2482, 2483, ... |
94 | 6, 7, 17, 90, 126, 139, 143, 257, 293, 295, 319, 328, 387, 482, 519, 603, 720, 751, 819, 884, 896, 903, 905, 921, 952, 954, 956, 1042, 1058, 1147, 1170, 1237, 1253, 1279, 1295, 1343, 1366, 1370, 1406, 1465, 1514, 1593, 1595, 1607, 1609, 1622, 1701, 1705, 1709, 1736, 1772, 1791, 1833, 1860, 1866, 1879, 1969, 1990, 1992, 2059, 2115, 2132, 2169, 2219, 2233, 2253, 2344, ... |
95 | 44, 47, 66, 155, 187, 344, 345, 448, 492, 525, 546, 611, 642, 704, 721, 748, 820, 858, 1062, 1108, 1112, 1195, 1277, 1314, 1453, 1558, 1597, 1667, 1725, 1760, 1780, 1793, 1807, 1901, 1963, 1983, 2021, 2055, 2060, 2251, 2266, 2331, ... |
96 | 4, 19, 28, 36, 44, 79, 94, 106, 109, 125, 132, 147, 319, 343, 399, 412, 415, 435, 441, 449, 463, 491, 562, 576, 625, 643, 646, 649, 691, 701, 712, 787, 788, 820, 824, 840, 851, 976, 994, 1047, 1079, 1111, 1112, 1136, 1195, 1216, 1219, 1225, 1291, 1309, 1339, 1359, 1425, 1456, 1466, 1520, 1525, 1533, 1540, 1543, 1601, 1633, 1668, 1679, 1738, 1744, 1746, 1789, 1854, 1873, 1922, 2056, 2101, 2110, 2159, 2225, 2266, 2267, 2286, 2301, 2320, 2346, 2378, 2395, 2424, 2468, 2488, ... |
97 | 12, 90, 104, 234, 271, 339, 420, 421, 428, 429, 464, 805, 909, 934, 1054, 1114, 1116, 1128, 1144, 1159, 1193, 1364, 1788, 2086, 2215, 2254, 2448, 2461, ... |
98 | 2, 19, 20, 40, 52, 75, 80, 88, 95, 98, 100, 103, 106, 123, 124, 162, 176, 198, 220, 276, 311, 358, 396, 427, 429, 522, 525, 529, 555, 576, 586, 605, 675, 695, 733, 782, 811, 833, 872, 879, 891, 898, 950, 952, 971, 977, 982, 1076, 1090, 1150, 1156, 1219, 1231, 1257, 1260, 1312, 1340, 1483, 1621, 1707, 1716, 1742, 1774, 1806, 1810, 1847, 1850, 1926, 1935, 1975, 2019, 2042, 2090, 2153, 2167, 2169, 2238, 2260, 2262, 2306, 2346, 2356, 2451, 2474, ... |
99 | 63, 88, 113, 123, 134, 146, 217, 284, 320, 352, 504, 511, 532, 544, 603, 704, 802, 840, 870, 974, 1205, 1242, 1278, 1414, 1441, 1471, 1516, 1579, 1660, 1740, 1763, 1765, 1846, 1874, 1889, 1932, 1939, 1980, 2095, 2132, 2136, 2396, 2493, ... |
100 | 20, 22, 88, 106, 114, 133, 179, 189, 222, 224, 234, 312, 326, 333, 355, 440, 443, 492, 509, 535, 615, 676, 727, 751, 765, 767, 812, 813, 845, 925, 988, 1032, 1089, 1106, 1229, 1249, 1259, 1281, 1323, 1343, 1434, 1435, 1461, 1482, 1536, 1621, 1649, 1678, 1692, 1739, 1779, 1824, 1979, 2020, 2021, 2033, 2052, 2164, 2186, 2322, 2391, 2418, 2438, 2457, ... |
primer p | bases tales que p es primo único |
2 | 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, ... |
3 | 2, 4, 5, 8, 10, 11, 17, 23, 26, 28, 35, 47, 53, 71, 80, 82, 95, 107, 143, 161, 191, 215, 242, 244, 287, 323, 383, 431, 485, 575, 647, 728, 730, 767, 863, 971, 1151, 1295, 1457, 1535, 1727, 1943, 2186, 2188, 2303, 2591, 2915, 3071, 3455, 3887, 4373, 4607, 5183, 5831, 6143, 6560, 6562, 6911, 7775, 8747, 9215, 10367, 11663, 12287, 13121, 13823, 15551, 17495, 18431, 19682, 19684, 20735, 23327, 24575, 26243, 27647, 31103, 34991, 36863, 39365, 41471, 46655, 49151, 52487, 55295, 59048, 59050, 62207, 69983, 73727, 78731, 82943, 93311, 98303, 104975, 110591, 118097, 124415, 139967, 157463, 165887, 177146, 177148, 186623, 196607, 209951, 221183, 236195, 248831, 279935, 294911, 314927, 331775, 354293, 373247, 393215, 419903, 442367, 472391, 497663, 5398, 551440, 531471 629855, 663551, 708587, 746495, 786431, 839807, 884735, 944783, 995327, ... |
5 | 2, 3, 4, 6, 7, 9, 19, 24, 26, 39, 49, 79, 99, 124, 126, 159, 199, 249, 319, 399, 499, 624, 626, 639, 799, 999, 1249, 1279, 1599, 1999, 2499, 2559, 3124, 3126, 3199, 3999, 4999, 5119, 6249, 6399, 7999, 9999, 10239, 12499, 12799, 15624, 15626, 15999, 19999, 20479, 24999, 25599, 31249, 31999, 39999, 40959, 49999, 51199, 62499, 63999, 78124, 78126, 79999, 81919, 99999, 102399, 124999, 127999, 156249, 159999, 163839, 199999, 204799, 249999, 255999 312499, 319999, 327679, 390624, 390626, 399999, 409599, 499999, 511999, 624999, 639999, 655359, 781249, 799999, 819199, 999999, ... |
7 | 2, 3, 4, 5, 6, 8, 13, 18, 19, 27, 48, 50, 55, 97, 111, 195, 223, 342, 344, 391, 447, 685, 783, 895, 1371, 1567, 1791, 2400, 2402, 2743, 3135, 3583, 4801, 5487, 6271, 7167, 9603, 10975, 12543, 14335, 16806, 16808, 19207, 21951, 25087, 28671, 33613, 38415, 43903, 50175, 57343, 67227, 76831, 87807, 100351, 114687, 117648, 117650, 134455, 153663, 175615, 200703, 229375, 235297, 268911, 307327, 351231, 401407, 458751, 470595, 537823, 614655, 70246342, 70246342 823544, 917503, 941191, ... |
11 | 2, 3, 10, 12, 21, 43, 87, 120, 122, 175, 241, 351, 483, 703, 967, 1330, 1332, 1407, 1935, 2661, 2815, 3871, 5323, 5631, 7743, 10647, 11263, 14640, 14642, 15487, 21295, 22527, 29281, 30975, 42591, 45055, 58563, 61951, 85183, 90111, 117127, 123903, 161050, 161052, 170367, 180223, 234255, 247807, 322101, 340735, 360447, 468511, 495615, 644203, 681471, 720895, 937023, 991231, ... |
13 | 2, 3, 4, 5, 12, 14, 22, 23, 25, 51, 103, 168, 170, 207, 239, 337, 415, 675, 831, 1351, 1663, 2196, 2198, 2703, 3327, 4393, 5407, 6655, 8787, 10815, 13311, 17575, 21631, 26623, 28560, 28562, 35151, 43263, 53247, 57121, 70303, 86527, 106495, 114243, 140607, 173055, 212991, 228487, 281215, 346111, 371292, 371294, 425983, 456975, 562431, 692223, 742585, 851967, 913951, ... |
17 | 2, 4, 16, 18, 33, 67, 135, 271, 288, 290, 543, 577, 1087, 1155, 2175, 2311, 4351, 4623, 4912, 4914, 8703, 9247, 9825, 17407, 18495, 19651, 34815, 36991, 39303, 69631, 73983, 78607, 83520, 83522, 139263, 147967, 157215, 167041, 278527, 295935, 314431, 334083, 557055, 591871, 628863, 668167, ... |
19 | 2, 7, 8, 18, 20, 37, 75, 151, 303, 360, 362, 607, 721, 1215, 1443, 2431, 2887, 4863, 5775, 6858, 6860, 9727, 11551, 13717, 19455, 23103, 27435, 38911, 46207, 54871, 77823, 92415, 109743, 130320, 130322, 155647, 184831, 219487, 260641, 311295, 369663, 438975, 521283, 622591, 739327, 877951, ... |
23 | 22, 24, 45, 91, 183, 367, 528, 530, 735, 1057, 1471, 2115, 2943, 4231, 5887, 8463, 11775, 12166, 12168, 16927, 23551, 24333, 33855, 47103, 48667, 67711, 94207, 97335, 135423, 188415, 194671, 270847, 279840, 279842, 376831, 389343, 541695, 559681, 753663, 778687, ... |
29 | 28, 30, 41, 57, 115, 231, 463, 840, 842, 927, 1681, 1855, 3363, 3711, 6727, 7423, 13455, 14847, 24388, 24390, 26911, 29695, 48777, 53823, 59391, 97555, 107647, 118783, 195111, 215295, 237567, 390223, 430591, 475135, 707280, 707282, 780447, 861183, 950271, ... |
31 | 2, 5, 6, 30, 32, 61, 123, 247, 495, 960, 962, 991, 1921, 1983, 3843, 3967, 7687, 7935, 15375, 15871, 29790, 29792, 30751, 31743, 59581, 61503, 63487, 119163, 123007, 126975, 238327, 246015, 253951, 476655, 492031, 507903, 923520, 923522, 953311, 984063, ... |
37 | 6, 10, 11, 36, 38, 73, 147, 295, 591, 1183, 1368, 1370, 2367, 2737, 4735, 5475, 9471, 10951, 18943, 21903, 37887, 43807, 50652, 50654, 75775, 87615, 101305, 151551, 175231, 202611, 303103, 350463, 405223, 606207, 700927, 810447, ... |
41 | 2, 3, 4, 9, 40, 42, 81, 163, 327, 655, 1311, 1680, 1682, 2623, 3361, 5247, 6723, 10495, 13447, 20991, 26895, 41983, 53791, 68920, 68922, 83967, 107583, 137841, 167935, 215167, 275683, 335871, 430335, 551367, 671743, 860671, ... |
43 | 2, 6, 7, 42, 44, 85, 171, 343, 687, 1375, 1848, 1850, 2751, 3697, 5503, 7395, 11007, 14791, 22015, 29583, 44031, 59167, 79506, 79508, 88063, 118335, 159013, 176127, 236671, 318027, 352255, 473343, 636055, 704511, 946687, ... |
47 | 46, 48, 93, 187, 375, 751, 1503, 2208, 2210, 3007, 4417, 6015, 8835, 12031, 17671, 24063, 35343, 48127, 70687, 96255, 103822, 103824, 141375, 192511, 207645, 282751, 385023, 415291, 565503, 770047, 830583, ... |
53 | 52, 54, 105, 211, 423, 847, 1695, 2808, 2810, 3391, 5617, 6783, 11235, 13567, 22471, 27135, 44943, 54271, 89887, 108543, 148876, 148878, 179775, 217087, 297753, 359551, 434175, 595507, 719103, 868351, ... |
59 | 58, 60, 117, 235, 471, 943, 1887, 3480, 3482, 3775, 6961, 7551, 13923, 15103, 27847, 30207, 55695, 60415, 111391, 120831, 205378, 205380, 222783, 241663, 410757, 445567, 483327, 821515, 891135, 966655, ... |
61 | 3, 11, 13, 14, 60, 62, 121, 243, 487, 975, 1951, 3720, 3722, 3903, 7441, 7807, 14883, 15615, 29767, 31231, 59535, 62463, 119071, 124927, 226980, 226982, 238143, 249855, 453961, 476287, 499711, 907923, 952575, 999423, ... |
67 | 66, 68, 133, 267, 535, 1071, 2143, 4287, 4488, 4490, 8575, 8977, 17151, 17955, 34303, 35911, 68607, 71823, 137215, 143647, 274431, 287295, 300762, 300764, 548863, 574591, 601525, ... |
71 | 70, 72, 141, 283, 567, 1135, 2271, 4543, 5040, 5042, 9087, 10081, 18175, 20163, 36351, 40327, 72703, 80655, 145407, 161311, 290815, 322623, 357910, 357912, 581631, 645247, 715821, ... |
73 | 2, 3, 8, 9, 72, 74, 145, 291, 583, 1167, 2335, 4671, 5328, 5330, 9343, 10657, 18687, 21315, 37375, 42631, 74751, 85263, 149503, 170527, 299007, 341055, 389016, 389018, 598015, 682111, 778033, ... |
79 | 78, 80, 157, 315, 631, 1263, 2527, 5055, 6240, 6242, 10111, 12481, 20223, 24963, 40447, 49927, 80895, 99855, 161791, 199711, 323583, 399423, 493038, 493040, 647167, 798847, 986077, ... |
83 | 82, 84, 165, 331, 663, 1327, 2655, 5311, 6888, 6890, 10623, 13777, 21247, 27555, 42495, 55111, 84991, 110223, 169983, 220447, 339967, 440895, 571786, 571788, 679935, 881791, ... |
89 | 88, 90, 177, 355, 711, 1423, 2847, 5695, 7920, 7922, 11391, 15841, 22783, 31683, 45567, 63367, 91135, 126735, 182271, 253471, 364543, 506943, 704968, 704970, 729087, ... |
97 | 96, 98, 193, 387, 775, 1551, 3103, 6207, 9408, 9410, 12415, 18817, 24831, 37635, 49663, 75271, 99327, 150543, 198655, 301087, 397311, 602175, 794623, 912672, 912674, ... |
Bibliografía
- Chris K. Caldwell, Harvey Dubner, "números primos de un período único", preimpresión de Journal of Recreational Mathematics 29 : 1: 43-48 (1998)
Referencias
- ^ Caldwell, Chris. "Prima única" . Las Prime Pages . Consultado el 11 de abril de 2014 .
- ^ Registros PRP: Probable Primes Top 10000
- ^ Los veinte mejores únicos ; Chris Caldwell
- ^ Registros PRP
- ^ El proyecto Cunningham
- ^ Registros PRP
- Yates, Samuel (1980). "Periodos de primos únicos". Matemáticas. Mag . 53 : 314. Zbl 0445.10009 .
enlaces externos
- Prime Top Tens
- Primas de período único
- Factorización de números de repetición