Re: [Prime] Tip: 2^31-1 = Mersenne exponent

[Guido Smetrijns]

I don't think so... In my opinion this is only a very wild guess and does not really show any underlying scientific thoughts... Any amateur could come up with silly "conjectures" like this. For example: 2^(2^0)+1 = 2^1+1 =   3    (Fermat prime)     2^(2^3)+1 = 2^8+1 = 257  (Fermat prime) So, 2^(2^257)+1 is probably a new Fermat prime !!! If you would be so kind to study the history of prime numbers for a couple of days or so, you would probably see that prime numbers won't let themselves be caught in such a simple formula like that. Please be a bit more modest next time and show the prime numbers the respect they deserve... Dr. med. Roland Linder wrote: Dear Prime community,   please be aware of the following:   2^2-1 = 3 (Mersenne prime)   2^3-1 = 7 (Mersenne prime)   2^7-1 = 127 (Mersenne prime)   2^127-1 = ca. 2.3E+18 (Mersenne prime)   2^ca. 2.3E+18 -1 = probably a further Mersenne prime   My hypothesis: Starting with one-digit primes, you can use a Mersenne prime as Mersenne exponent to yield a further Mersenne prime.   Because today we cannot proove the primarity of 2^ca. 2.3E+18 -1 let me suggest to investigate 2^31-1 as a Mersenne exponent:   2^5-1 = 31 (Mersenne prime)   2^31-1 = 2 147 483 647 (Mersenne prime)   2^2147483647-1 = Next Mersenne prime ?   Using a single PC it would take me about 600 years to check this. Using the GIMPS project it should be feasible.   What do you think about that?   Best regards, Dr. Roland Linder     __________ NOD32 1.1042 (20050331) Information __________ This message was checked by NOD32 antivirus system. http://www.nod32.com _______________________________________________ Prime mailing list Prime@hogranch.com http://hogranch.com/mailman/listinfo/prime __________ NOD32 1.1042 (20050331) Information __________ This message was checked by NOD32 antivirus system. http://www.nod32.com

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