>2^(q-1) mod q = 1 > >==comment== (q-1) is the number of integers less than q that is not a >factor of q plus the number 1 > >Then, 2^(q-1) -1 = x * q where x is any positive integer > >If N = 2^(q-1) - 1 = x * q > >then, N is a number with all binary digits equal to 1 and the number of >digits is EVEN (q-1). > >and N is the LOWEST VALUE of MULTIPLE of q with all binary digits equal to >1 (very important!!!) The last line in this chain of reasoning is false. Take q = 23. Yes, 2^22 mod 23 = 1, but 22 is not the lowest power of 2 where this is the case. 2^11 mod 23 = 1, so 11 is the lowest power of 2 which is congruent to 1 mod 23. Nick Glover: [EMAIL PROTECTED] Computer Science, Clemson University Homepage: http://hubcap.clemson.edu/~nglover/ "It's good to be open-minded, but not so open that your brains fall out." - Jacob Needleman _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
