Hace aproximadamente un año que me percaté de una relación
que existía entre la Sucesión del orden y la belleza: la Sucesión de Fibonacci de la cual se engendra el número áureo 1.618... y la distribución de los Números Primos.
Vamos empezando a modelar un esquema gráfico donde
visualmente nos percataremos de esa
misteriosa relación:
Si hacemos una lista horizontal de los elementos de la
Sucesión de Fibonacci y de manera paralela los números naturales, podemos verificar que a
partir del número primo 7 encontramos un
patrón de la siguiente manera:
Los números Primos de la lista de los Naturales
tienden a ser divisibles por los
elementos de la sucesión de Fibonacci en posiciones n+1 y n-1, vemos en el
gráfico el trazo de diagonales y generamos la siguiente tabla para hacer un
análisis:
Este patrón para
casi 10 primos nos permite intuir que se
puede cumplir al infinito, pero tenemos un pequeño inconveniente, la sucesión
de Fibonacci comienza a crecer considerablemente, por lo que nuestra capacidad
de cálculo nos obliga a hacer uso de un
software matemático para comprobar que
la tendencia se sigue produciendo en una
cantidad considerable antes de formular toda conjetura, y es cuando hacemos uso
de Wólfram Matemathica.
Comenzamos con la
siguiente expresión producto de la intuición:
Si Fibonacci(n+1) Mod (n) =0
y Fibonacci (n-1) Mod (n) =0, entonces ‘n’ es un número Primo.
Encontramos el primer contraejemplo para nuestra intuición,
para el caso n=323, el cual no es un
número primo, después observamos que la sucesión vuelve a retomar el
patrón.
No todo está perdido, si bien el patrón se rompe con un par
de contraejemplos, nuestro modelo
gráfico bautizado como la Criba de Fibonacci podría encontrar sin problema los primeros 66 números primos:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191, 193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283, 293,307,311,313,317… |
Al observar
que el patrón vuelve a recobrar sentido, podemos sacar provecho de este partido
y generar fórmulas que produzcan una cantidad de números primos considerables,
ese será nuestro punto de partida en este momento, nos fijamos una primer meta:
Conseguir una expresión matemática que
genere por lo menos a los primeros 100
números primos haciendo uso del patrón observado de la sucesión de
Fibonacci.
Al seguir trabajando en Wolfram Matemathica con las
tendencias antes encontradas para 700
valores de la variable ‘n’ y además de ir condicionando las fórmulas debido a
contraejemplos y parásitos encontrados,
llegamos a las siguientes expresiones donde se incluyen residuos, funciones
piso y funciones techo:
QUE CORRESPONDEN A LOS PRIMEROS 125 NÚMEROS PRIMOS.
SI APLICAMOS EN WOLFRAM MATEMATHICA A LA FÓRMULA ‘PRIMOS’ LA FUNCIÓN
DELETECASES PARA SUPRIMIR LOS CEROS Y SÓLO DEJAR LAS ENTIDADES PRIMALES, NOS
QUEDA:
PRIMOS=A+B+C+D+E+F+G
DeleteCases [PRIMOS, 0]
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173, 179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263, 269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359, 367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457, 461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569, 571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659, 661,673,677,683,691 |
NUESTRA FÓRMULA PRIMOS=A+B+C+D+E+F+G GENERA LOS PRIMEROS 125 NÚMEROS PRIMOS
NUEVA+NUEVA2+NUEVA3
EL RESULTADO:
NUEVA=
2,3,0,0,0,7,0,0,0,0,0,13,0,0,0,17,0,19,0,0,0,23,0,0,0,0,0,29,
0,31,0,0,0,0,0,37,0,0,0,41,0,43,0,0,0,47,0,0,0,0,0,53,0,0,0, 0,0,59,0,61,0,0,0,0,0,67,0,0,0,71,0,73,0,0,0,0,0,79,0,0,0,83, 0,0,0,0,0,89,0,0,0,0,0,0,0,97,0,0,0,101,0,103,0,0,0,107,0, 109,0,0,0,113,0,0,0,0,0,0,0,0,0,0,0,0,0,127,0,0,0,131,0,0, 0,0,0,137,0,139,0,0,0,0,0,0,0,0,0,149,0,151,0,0,0,0,0,157, 0,0,0,0,0,163,0,0,0,167,0,0,0,0,0,173,0,0,0,0,0,179,0,181, 0,0,0,0,0,0,0,0,0,191,0,193,0,0,0,197,0,199,0,0,0,0,0,0,0, 0,0,0,0,211,0,0,0,0,0,0,0,0,0,0,0,223,0,0,0,227,0,229,0,0, 0,233,0,0,0,0,0,239,0,241,0,0,0,0,0,0,0,0,0,251,0,0,0,0,0, 257,0,0,0,0,0,263,0,0,0,0,0,269,0,271,0,0,0,0,0,277,0,0,0, 281,0,283,0,0,0,0,0,0,0,0,0,293,0,0,0,0,0,0,0,0,0,0,0,0,0, 307,0,0,0,311,0,313,0,0,0,317,0,0,0,0,0,0,0,0,0,0,0,0,0, 331,0,0,0,0,0,337,0,0,0,0,0,0,0,0,0,347,0,349,0,0,0,353, 0,0,0,0,0,359,0,0,0,0,0,0,0,367,0,0,0,0,0,373,0,0,0,0,0, 379,0,0,0,383,0,0,0,0,0,389,0,0,0,0,0,0,0,397,0,0,0, 401,0,0,0,0,0,0,0,409,0,0,0,0,0,0,0,0,0,419,0,421,0,0,0, 0,0,0,0,0,0,431,0,433,0,0,0,0,0,439,0,0,0,443,0,0,0,0,
0,449,0,0,0,0,0,0,0,457,0,0,0,461,0,463,0,0,0,467,0,0,
0,0,0,0,0,0,0,0,0,479,0,0,0,0,0,0,0,487,0,0,0,491,0,0,0, 0,0,0,0,499,0,0,0,503,0,0,0,0,0,509,0,0,0,0,0,0,0,0,0,0, 0,521,0,523,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,541,0,0,0,0, 0,547,0,0,0,0,0,0,0,0,0,557,0,0,0,0,0,563,0,0,0,0,0,569, 0,571,0,0,0,0,0,577,0,0,0,0,0,0,0,0,0,587,0,0,0,0,0,593, 0,0,0,0,0,599,0,601,0,0,0,0,0,607,0,0,0,0,0,613,0,0,0, 617,0,619,0,0,0,0,0,0,0,0,0,0,0,631,0,0,0,0,0,0,0,0,0, 641,0,643,0,0,0,647,0,0,0,0,0,653,0,0,0,0,0,659,0,661, 0,0,0,0,0,0,0,0,0,0,0,673,0,0,0,677,0,0,0,0,0,683,0,0,0, 0,0,0,0,691,0,0,0,0,0,0,0,0,0,701,0,0,0,0,0,0,0,709,0,0, 0,0,0,0,0,0,0,719,0,0,0,0,0,0,0,727,0,0,0,0,0,733,0,0, 0,0,0,739,0,0,0,743,0,0,0,0,0,0,0,751,0,0,0,0,0,757,
0,0,0,761,0,0,0,0,0,0,0,769,0,0,0,773,0,0,0,0,0,0,0,0,
0,0,0,0,0,787,0,0,0,0,0,0,0,0,0,797,0,0,0,0,0,0,0,0,
0,0,0,809,0,811,0,0,0,0,0,0,0,0,0,821,0,823,0,0,0,827,
0,829,0,0,0,0,0,0,0,0,0,839,0,0,0,0,0,0,0,0,0,0,0,
0,0,853,0,0,0,857,0,859,0,0,0,863,0,0,0,0,0,0,0,0,
0,0,0,0,0,877,0,0,0,881,0,883,0,0,0,887,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,907,0,0,0,911,0,0,0,0,0,0,0, 919,0,0,0,0,0,0,0,0,0,929,0,0,0,0,0,0,0,937,0,0,0,941,
0,0,0,0,0,947,0,0,0,0,0,953,0,0,0,0,0,0,0,0,0,0,0,0,0,967,
0,0,0,971,0,0,0,0,0,977,0,0,0,0,0,983,0,0,0,0,0,
0,0,991,0,0,0,0,0,997,0,0,0,0,0,0,0,0,0,0,0,1009,0,0,0,
1013,0,0,0,0,0,1019,0,1021,0,0,0,0,0,0,0,0,0,
1031,0,1033,0,0,0,0,0,1039,0,0,0,0,0,0,0,0,0,1049,0,
1051,0,0,0,0,0,0,0,0,0,1061,0,1063,0,0,0,0,0,1069,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1087,0,0,0,1091,0,1093,
0,0,0,1097,0,0,0,0,0,1103,0,0,0,0,0,1109,0,0,0,
0,0,0,0,1117,0,0,0,0,0,1123,0,0,0,0,0,1129,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1151,0,1153,0,0,0,0,
0,0,0,0,0,1163,0,0,0,0,0,0,0,1171,0,0,0,0,0,0,0,0,0,1181
,0,0,0,0,0,1187,0,0,0,0,0,1193,0,0,0,0,0,0,0,1201,
0,0,0,0,0,0,0,0,0,0,0,1213,0,0,0,1217,0,0,0,0,0,1223,0,0,0,0,0,
1229,0,1231,0,0,0,0,0,1237,0,0,0,0,0,0,0,0,0,0,0,1249, 0,0,0,0,0,0,0,0,0,1259,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1277,0,1279,0,0,0,1283,0,0,0,0,0,1289,0,1291,0,0,0, 0,0,1297,0,0,0,1301,0,1303,0,0,0,1307,0,0,0,0,0,0,0, 0,0,0,0,1319,0,1321,0,0,0,0,0,1327,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1361,0,0,0,0,0,1367,0,0,0,0,0,1373,
0,0,0,0,0,0,0,1381
|
NUEVA2=
{0,0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
|
NUEVA3=
0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
|
EL RESULTADO FINAL:
2,3,0,5,0,7,0,0,0,11,0,13,0,0,0,17,0,19,0,0,0,
23,0,0,0,0,0,29,0,31,0,0,0,0,0,37,0,0,0,41,0,
43,0,0,0,47,0,0,0,0,0,53,0,0,0,0,0,59,0,61,0,
0,0,0,0,67,0,0,0,71,0,73,0,0,0,0,0,79,0,0,0,83,
0,0,0,0,0,89,0,0,0,0,0,0,0,97,0,0,0,101,0,103,
0,0,0,107,0,109,0,0,0,113,0,0,0,0,0,0,0,0,0,0,
0,0,0,127,0,0,0,131,0,0,0,0,0,137,0,139,0,0,
0,0,0,0,0,0,0,149,0,151,0,0,0,0,0,157,0,0,0,0,0,
163,0,0,0,167,0,0,0,0,0,173,0,0,0,0,0,179,0,
181,0,0,0,0,0,0,0,0,0,191,0,193,0,0,0,197,0, 199,0,0,0,0,0,0,0,0,0,0,0,211,0,0,0,0,0,0,0, 0,0,0,0,223,0,0,0,227,0,229,0,0,0,233,0,0, 0,0,0,239,0,241,0,0,0,0,0,0,0,0,0,251,0,0,0, 0,0,257,0,0,0,0,0,263,0,0,0,0,0,269,0,271,0,0,0,0,0,277,
0,0,0,281,0,283,0,0,0,0,0,0,0,0,0,293,0,0,0,0,
0,0,0,0,0,0,0,0,0,307,0,0,0,311,0,313,0,0,0,317,
0,0,0,0,0,0,0,0,0,0,0,0,0,331,0,0,0,0,0,337,0,0,
0,0,0,0,0,0,0,347,0,349,0,0,0,353,0,0,0,0,0,359,
0,0,0,0,0,0,0,367,0,0,0,0,0,373,0,0,0,0,0,379,
0,0,0,383,0,0,0,0,0,389,0,0,0,0,0,0,0,397,0,0,0,
401,0,0,0,0,0,0,0,409,0,0,0,0,0,0,0,0,0,419,0,
421,0,0,0,0,0,0,0,0,0,431,0,433,0,0,0,0,0,439,
0,0,0,443,0,0,0,0,0,449,0,0,0,0,0,0,0,457,0,0,
0,461,0,463,0,0,0,467,0,0,0,0,0,0,0,0,0,0,0,479,
0,0,0,0,0,0,0,487,0,0,0,491,0,0,0,0,0,0,0,499,0,
0,0,503,0,0,0,0,0,509,0,0,0,0,0,0,0,0,0,0,0,521,
0,523,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,541,0,0,0,
0,0,547,0,0,0,0,0,0,0,0,0,557,0,0,0,0,0,563,
0,0,0,0,0,569,0,571,0,0,0,0,0,577,0,0,0,0,0,0,0,
0,0,587,0,0,0,0,0,593,0,0,0,0,0,599,0,601,0,
0,0,0,0,607,0,0,0,0,0,613,0,0,0,617,0,619,0,0,0,
0,0,0,0,0,0,0,0,631,0,0,0,0,0,0,0,0,0,641,0,
643,0,0,0,647,0,0,0,0,0,653,0,0,0,0,0,659,0,661,
0,0,0,0,0,0,0,0,0,0,0,673,0,0,0,677,0,0,0,0,0,
683,0,0,0,0,0,0,0,691,0,0,0,0,0,0,0,0,0,701,0,0,0,
0,0,0,0,709,0,0,0,0,0,0,0,0,0,719,0,0,0,0,0,0
,0,727,0,0,0,0,0,733,0,0,0,0,0,739,0,0,0,743,0,0,0,
0,0,0,0,751,0,0,0,0,0,757,0,0,0,761,0,0,0,0,0,
0,0,769,0,0,0,773,0,0,0,0,0,0,0,0,0,0,0,0,0,787,0,0,
0,0,0,0,0,0,0,797,0,0,0,0,0,0,0,0,0,0,0,809,0,
811,0,0,0,0,0,0,0,0,0,821,0,823,0,0,0,827,0,829,0,
0,0,0,0,0,0,0,0,839,0,0,0,0,0,0,0,0,0,0,0,0,0,
853,0,0,0,857,0,859,0,0,0,863,0,0,0,0,0,0,0,0,0,0,
0,0,0,877,0,0,0,881,0,883,0,0,0,887,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,907,0,0,0,911,0,0,0,0,0,
0,0,919,0,0,0,0,0,0,0,0,0,929,0,0,0,0,0,0,0,937,
0,0,0,941,0,0,0,0,0,947,0,0,0,0,0,953,0,0,0,0,0,0,0,
0,0,0,0,0,0,967,0,0,0,971,0,0,0,0,0,977,0,0,0,0,
0,983,0,0,0,0,0,0,0,991,0,0,0,0,0,997,0,0,0,0,0,0,0,
0,0,0,0,1009,0,0,0,1013,0,0,0,0,0,1019,0,1021,
0,0,0,0,0,0,0,0,0,1031,0,1033,0,0,0,0,0,1039,0,0,0,
0,0,0,0,0,0,1049,0,1051,0,0,0,0,0,0,0,0,0,1061,
0,1063,0,0,0,0,0,1069,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1087,0,0,0,1091,0,1093,0,0,0,1097,0,0,0,0,
0,1103,0,0,0,0,0,1109,0,0,0,0,0,0,0,1117,0,0,0,0,0,1123,
0,0,0,0,0,1129,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1151,0,1153,0,0,0,0,0,0,0,0,0,1163,0,0,
0,0,0,0,0,1171,0,0,0,0,0,0,0,0,0,1181,0,0,0,0,0,
1187,0,0,0,0,0,1193,0,0,0,0,0,0,0,1201,0,0,0,0,0,0,
0,0,0,0,0,1213,0,0,0,1217,0,0,0,0,0,1223,0,0,0,0,
0,1229,0,1231,0,0,0,0,0,1237,0,0,0,0,0,0,0,0,0,0,0,
1249,0,0,0,0,0,0,0,0,0,1259,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1277,0,1279,0,0,0,1283,0,0,0,0,0,1289,
0,1291,0,0,0,0,0,1297,0,0,0,1301,0,1303,0,0,0,
1307,0,0,0,0,0,0,0,0,0,0,0,1319,0,1321,0,0,0,0,0,1327,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1361,0,0,0,0,0,1367,0,0,0,0,0,
1373,0,0,0,0,0,0,0,1381 |
Borramos Ceros:
DeleteCases [nueva+nueva2+nueva3, 0 ]
{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,
281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,
389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,
491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,
607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,
719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,
829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,
953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,
1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,
1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,
1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,
1367,1373,1381}
|
OBTENEMOS LOS PRIMEROS 221 NÚMEROS
PRIMOS
AUTOR:
M.M e ING. José de Jesús Camacho
Medina
Fresnillo Zacatecas, México - Febrero
de 2013
No hay comentarios:
Publicar un comentario