----- Original Message -----
From: "George Woltman" <[EMAIL PROTECTED]>
To: "Daran" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Thursday, December 05, 2002 2:35 AM
Subject: Re: Mersenne: P-1 and non k-smooth factors
> The analysis is more complex than this...
I never doubted that. :-)
[...]
> Why not take your example:
> "on an 8.1M exponent, B1=45000,
> B2=731250 and varying values for D and E, I get the following
results
> D E Stage 2 transforms
> 420 2 93946
> 420 4 98618 (the default for my memory settings)"
Done one more:
420 6 103746
It's looking very linear.
> and write a program that emulates stage 2's selection of (x^E - d^E), does
> a prime factorization of the value, and keeps track of which factors above
> B2 get included. It should be possible to calculate your increased chance
> of finding a factor (someone please fill in the formula here).
That's a rather more extensive programming job than the one I had in mind.
It would also be expensive at runtime, with a prime factorisation in every
cycle.
What I was thinking of, is to take the k of known Mersenne factors, or at
Brian's suggestion, random integers of an appropriate size, factor them to
obtain the second largest and largest factor, a and b, say, then emulate the
stage 2 selection of (x^E - d^E) from B1=a through to B2=b or until I find
one divisible by b, which ever comes first.
Regards
Daran
_________________________________________________________________________
Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
