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Old 2007-07-21, 08:21   #1
Brian-E's Avatar
Jul 2007
The Netherlands

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Default Status of GIMPS proofs

If I've understood things - but please correct me if I'm wrong or incomplete - GIMPS aims to discover and prove three aspects of Mersenne numbers:

(1) Discover new Mersenne Primes
(2) Prove that there are no lower Mersenne Primes than the ones already discovered
(3) For composite Mersenne numbers with accessible factor(s) find the lowest factor

(1) and (3) are clearly relatively easy to verify by the Mathematical community because they involve individual Mersenne numbers. But what about (2)? It is not really independently verifiable that what GIMPS now calls M39 is the 39th Mersenne because no-one can run tens of thousands of computers for another 10 years.

My question is: is there feedback, positive or negative, by independent Mathematicians about the status of GIMPS' findings about the number of Mersenne Primes in particular exponent ranges? Are the safeguards (the double checking of Lucas Lehmer tests and requirement of two tests with the same final residue) generally accepted as proof by the general Mathematical community or is there some controversy? I've seen only positive references to GIMPS on the internet by the way.
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