another p-1 question

jocelynl · 2006-01-18, 03:51

P-1 usually finds smooth factor with gcd of 3^n! and 2^P-1

ex: p=67 N=2^p-1
a factor of N is 193707721 which 2*2*2*3*3*3*5*67*2677+1
So the gcd of 3^(2*2*2*3*3*3*5*67*2677) and N is 193707721

but there is also 3^(2*2*17*17*41*61*67+(4*67))

Has any work been do to find an algorythm like P-1 capable of finding smoother factors?

Joss

2006-01-18, 03:51	#1
jocelynl Sep 2002 262₁₀ Posts	another p-1 question P-1 usually finds smooth factor with gcd of 3^n! and 2^P-1 ex: p=67 N=2^p-1 a factor of N is 193707721 which 2223335672677+1 So the gcd of 3^(2223335672677) and N is 193707721 but there is also 3^(221717416167+(4*67)) Has any work been do to find an algorythm like P-1 capable of finding smoother factors? Joss