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## RE: [PrimeNumbers] Find the next prime

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• If 2^n+1 is prime, n must be a power of 2 (2^0, 2^1, ...) and only the five are known. So for 2^((p-1)/2) + 1 to be prime, p must also be a Fermat prime. CC
Message 1 of 69 , Sep 30, 2008
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If 2^n+1 is prime, n must be a power of 2 (2^0, 2^1, ...) and only the five are known.

So for 2^((p-1)/2) + 1 to be prime, p must also be a Fermat prime.

CC

-----Original Message-----
From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On Behalf Of Sebastian Martin Ruiz
Sent: Tuesday, September 30, 2008 11:41 AM
Subject: [PrimeNumbers] Find the next prime

Hello all:

2^((pn-1)/2) + 1 is prime for n=2,3,7 (the primes are 3, 5, 257)

Find the next. (Are all Fermat Primes?)

Sincerely

Sebastián Martin Ruiz

[Non-text portions of this message have been removed]

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• ... Congrats! That size of 15537 digits is nearly 25% bigger than the next 12 on that Top-20 Lehmer Primitive Part list, which all date from more than 3
Message 69 of 69 , May 10, 2009
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>
> --- In primenumbers@yahoogroups.com,
>
> > The Society for Suppression of Square Roots hopes to
> > be able to announce, within a few days, the proof of
> > a unique Lehmer prime with more than 15000 digits
> > (wenn die Frau Göttin probiert hat).
> > If proven, it will also become the largest known prime at
> > http://primes.utm.edu/top20/page.php?id=68
>
> Consummatus est in brevi explevit tempora multa [Wisdom:4:13]
>