saludos, pues no se si tan de esta casa soy pero algo te puedo orientar
http://sourceforge.net/projects/msieve/?source=dlpel programa es de codigo libre, se baja de ahi, la gui es para factorizar un numero en valores primos(osea factorizar 15 es 3*5 , ese sera el resultado)
en cuanto al uso, tambien existe un GUI (o aspecto visual), solo configurando un poco mas el tema del largo, usando los valores en decimal
http://tuts4you.com/download.php?view.1252pero debes renombrar msieve150.exe a msieve.exe
luego obviamente se crea un .ini con el valor a factorizar ejemplo:
worktodo.inique contiene
51721252920701396209200934332086955610172597582924827043466937307507316773473
este numero al ser factorizado
da un resultado: en un formato mas o menos esto
p2= significa que es un primo de 2 digitos
p3= es un primo de 3 digitos..y asi suma y sigue
Tue Dec 18 12:19:57 2012 Msieve v. 1.50 (SVN 708)
Tue Dec 18 12:19:57 2012 random seeds: ba098b04 f16f1b7d
Tue Dec 18 12:19:57 2012 factoring 51721252920701396209200934332086955610172597582924827043466937307507316773473 (77 digits)
Tue Dec 18 12:19:57 2012 searching for 15-digit factors
Tue Dec 18 12:19:57 2012 commencing quadratic sieve (70-digit input)
Tue Dec 18 12:19:57 2012 using multiplier of 5
Tue Dec 18 12:19:57 2012 using 32kb Intel Core sieve core
Tue Dec 18 12:19:57 2012 sieve interval: 12 blocks of size 32768
Tue Dec 18 12:19:57 2012 processing polynomials in batches of 17
Tue Dec 18 12:19:57 2012 using a sieve bound of 208553 (9343 primes)
Tue Dec 18 12:19:57 2012 using large prime bound of 19395429 (24 bits)
Tue Dec 18 12:19:57 2012 using trial factoring cutoff of 24 bits
Tue Dec 18 12:19:57 2012 polynomial 'A' values have 9 factors
Tue Dec 18 12:21:19 2012 10020 relations (4716 full + 5304 combined from 54935 partial), need 9439
Tue Dec 18 12:21:19 2012 begin with 59651 relations
Tue Dec 18 12:21:19 2012 reduce to 14667 relations in 2 passes
Tue Dec 18 12:21:19 2012 attempting to read 14667 relations
Tue Dec 18 12:21:19 2012 recovered 14667 relations
Tue Dec 18 12:21:19 2012 recovered 12070 polynomials
Tue Dec 18 12:21:19 2012 attempting to build 10020 cycles
Tue Dec 18 12:21:19 2012 found 10020 cycles in 1 passes
Tue Dec 18 12:21:19 2012 distribution of cycle lengths:
Tue Dec 18 12:21:19 2012 length 1 : 4716
Tue Dec 18 12:21:19 2012 length 2 : 5304
Tue Dec 18 12:21:19 2012 largest cycle: 2 relations
Tue Dec 18 12:21:19 2012 matrix is 9343 x 10020 (1.3 MB) with weight 291116 (29.05/col)
Tue Dec 18 12:21:19 2012 sparse part has weight 291116 (29.05/col)
Tue Dec 18 12:21:19 2012 filtering completed in 3 passes
Tue Dec 18 12:21:19 2012 matrix is 7533 x 7596 (1.0 MB) with weight 232889 (30.66/col)
Tue Dec 18 12:21:19 2012 sparse part has weight 232889 (30.66/col)
Tue Dec 18 12:21:19 2012 commencing Lanczos iteration
Tue Dec 18 12:21:19 2012 memory use: 1.1 MB
Tue Dec 18 12:21:20 2012 lanczos halted after 121 iterations (dim = 7531)
Tue Dec 18 12:21:20 2012 recovered 64 nontrivial dependencies
Tue Dec 18 12:21:20 2012 p2 factor: 19
Tue Dec 18 12:21:20 2012 p3 factor: 137
Tue Dec 18 12:21:20 2012 p5 factor: 16759
Tue Dec 18 12:21:20 2012 prp26 factor: 14267903379230936196988283
Tue Dec 18 12:21:20 2012 prp44 factor: 83097241687915830157590489510383084457330703
Tue Dec 18 12:21:20 2012 elapsed time 00:01:23
otra herramienta que te puede ayudar a crear cosas de rsa es
http://tuts4you.com/download.php?view.455 estos trabajan con primos grandes..
hagamos otro ejemplo
lo que esto muestra
http://foro.elhacker.net/net/aporte_factorizacion_relativamente_rapida_actualizado_18082012-t321927.0.htmltambien puede ser usado, y obtiene estos resultados:
Tue Dec 18 12:29:43 2012 Msieve v. 1.50 (SVN 708)
Tue Dec 18 12:29:43 2012 random seeds: 0813c4d0 41b1d732
Tue Dec 18 12:29:43 2012 factoring 79228162514264337593543950335 (29 digits)
Tue Dec 18 12:29:43 2012 p1 factor: 3
Tue Dec 18 12:29:43 2012 p1 factor: 3
Tue Dec 18 12:29:43 2012 p1 factor: 5
Tue Dec 18 12:29:43 2012 p1 factor: 7
Tue Dec 18 12:29:43 2012 p2 factor: 13
Tue Dec 18 12:29:43 2012 p2 factor: 17
Tue Dec 18 12:29:43 2012 p2 factor: 97
Tue Dec 18 12:29:43 2012 p3 factor: 193
Tue Dec 18 12:29:43 2012 p3 factor: 241
Tue Dec 18 12:29:43 2012 p3 factor: 257
Tue Dec 18 12:29:43 2012 p3 factor: 673
Tue Dec 18 12:29:43 2012 p5 factor: 65537
Tue Dec 18 12:29:43 2012 p8 factor: 22253377
Tue Dec 18 12:29:43 2012 elapsed time 00:00:00
ahora bien ese ultimo ejemplo si bien parece facil, puedes complementarlo con otras calculadoras cercanas
http://www.wolframalpha.com/input/?i=prime+factor+79228162514264337593543950335
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