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May 18

Smallest prime factor of 2^1277 - 1

Has anyone yet found the smallest prime factor of 2^1277 - 1?? Georgia guy (talk) 16:36, 18 May 2016 (UTC)[reply]

No factors are listed here, so probably not. -- BenRG (talk) 19:28, 18 May 2016 (UTC)[reply]

Is there a @PrimeHunter: in the house? (Probably won't give a different answer from Ben's, but might shed more light on this issue). -- Meni Rosenfeld (talk) 23:59, 18 May 2016 (UTC)[reply]

No factors are known. It's the smallest Mersenne number without a known factor. Based on http://www.mersenne.org/report_ECM/ the smallest factor probably has more than 60 digits but ECM gives no guarantees, and if a factor is found it isn't known whether it's the smallest unless the number is completely factored. Integer factorization records#Numbers of a special form mentions some of the work to factor smaller Mersenne numbers. One project used around 7500 core years. PrimeHunter (talk) 00:33, 19 May 2016 (UTC)[reply]

Can I have some free links to references on solving Laplace equation and legendary polynomials?Sayan19ghosh99 (talk) 17:05, 18 May 2016 (UTC)[reply]

I prefer the OP's version, as it could lead to some hit-or-myth methods of solution.→86.176.133.85 (talk) 16:49, 24 May 2016 (UTC)[reply]