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Message boards : Sophie Germain Prime Search : 2p-1?

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Bur
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Message 149246 - Posted: 8 Mar 2021 | 19:14:42 UTC

Is there something special about primes p where 2p-1 is also prime? They aren't rare apparently: 2 and 3, 3 and 5, 7 and 13, 19 and 37 or 307 and 613.

q = 2p-1 fulfills one half of the "strong prime" requirement in cryptography, i.e. q+1 has only large prime factors, same as for SG q-1 does.

It could be applied to Proth primes:

k * 2^n + 1 = p
k * 2^(n+1) + 1 = 2p - 1

So why aren't they investigated the same? Once more I guess I'm missing something, but what? :)
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Yves Gallot
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Message 149261 - Posted: 8 Mar 2021 | 23:17:18 UTC - in response to Message 149246.
Last modified: 8 Mar 2021 | 23:17:45 UTC

Sophie Germain primes are related to the first case of Fermat's last theorem, but Cunningham chains of the second kind have no known mathematical property.
See https://primes.utm.edu/top20/page.php?id=20

JeppeSN

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Message 149263 - Posted: 8 Mar 2021 | 23:41:21 UTC - in response to Message 149261.

Sophie Germain primes are related to the first case of Fermat's last theorem, but Cunningham chains of the second kind have no known mathematical property.
See https://primes.utm.edu/top20/page.php?id=20

Ooh, I like #3 and #4 on that top five. /JeppeSN

Bur
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Message 149287 - Posted: 9 Mar 2021 | 14:31:43 UTC

Ok, thanks.
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Message boards : Sophie Germain Prime Search : 2p-1?