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Old 2010-11-03, 16:12   #2
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

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Note that all primes above 3 are either 1 or 5 mod 6.
Originally Posted by science_man_88
I know that according to resource on the divisors of Mersenne numbers of prime index that aren't prime are +1/-1 mod 8 and of the form 2kp+1 which limits possible k values depending on the exponent mod 8 . I've look at all divisors of the exceptions to 2^37-1 so far it seems if p mod 6 =5 or 1 then 2 of the factors of 2^p-1 seem to be also the same modulo 6 is this verifiable if so could this be used to further reduce the k values needed to be checked ?
Another way to write 5 mod 6 is -1 mod 6. When p is odd, 2^p-1 is 1 mod 6.
If N is 1 mod 6, then there must be an even number of factors that are -1 mod 6 (because the factors mod 6 have to multiply to the number mod 6). As far as I can tell, this can't be used to make it easier to find factors.
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