----- Original Message ----- From: "Alexander Kruppa" <[EMAIL PROTECTED]> To: "Daran" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Wednesday, September 25, 2002 12:03 AM Subject: Re: Mersenne: P-1 and non k-smooth factors
> This is the Brent-Suyama extension, aka Suyama's powers. In short, if > you choose a Suyama's power E, a factor f will be found if the largest > factor of f-1 divides some (mD)^E - d^E, where D is an integer chosen > according to available memory, m and d are integers so that B1 < mD-d <= > B2, 1 <= d < D and mD-d is prime. [...] > ...the choice of D and E depends on the > implementation. Prime95 chooses D so that phi(D)+E+4 (phi() is Euler's > totient function) residues fit into memory, and chooses E like this: > > if (D <= 180) E = 2; > else if (D <= 420) E = 4; > else if (D <= 2310) E = 12; > else if (D <= 6930) E = 30; > else E = 48; > > (see ecm.c, choose_pminus1_plan() ) I understand why it chooses the values of D that it does, but why these values of E? I understand why E must be even, and that higher powers ought to be highly composite, but wouldn't 6 be a good intermediate value? 24? 60 for the top end? > Alex Daran _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
