Andy Hedges <[EMAIL PROTECTED]> asks:
> Anyone have any idea why for k = 659 there are very little primes? In fact
> for k up to 200000 there are none (I haven't found any in this range yet!).
Let k = 659.
If n == 1 (mod 2) then k*2^n == 1 (mod 3)
If n == 2 (mod 4) then k*2^n == 1 (mod 5)
If n == 0 (mod 3) then k*2^n == 1 (mod 7)
If n == 4 (mod 12) then k*2^n == 1 (mod 13)
If n == 8 (mod 9) then k*2^n == 1 (mod 73)
Therefore, if k*2^n - 1 is prime, then n == 20 or 32 (mod 36).
Other useful congruences include
If n == 2 (mod 5) then k*2^n == 1 (mod 31)
if n == 0 (mod 23) then k*2^n == 1 (mod 47)
This doesm't explain the total lack of primes, but
shows that many potential n can be eliminated early.
_________________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
