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

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Profile BurProject donor
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Joined: 25 Feb 20
Posts: 459
ID: 1241833
Credit: 278,570,989
RAC: 692,423
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Amethyst: Earned 1,000,000 credits (1,794,576)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Ruby: Earned 2,000,000 credits (4,999,193)AP 26/27 Ruby: Earned 2,000,000 credits (3,610,399)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
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? :)
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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

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Posts: 1532
ID: 306875
Credit: 35,596,887
RAC: 10,325
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,130,274)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
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

Profile BurProject donor
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Joined: 25 Feb 20
Posts: 459
ID: 1241833
Credit: 278,570,989
RAC: 692,423
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Amethyst: Earned 1,000,000 credits (1,794,576)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Ruby: Earned 2,000,000 credits (4,999,193)AP 26/27 Ruby: Earned 2,000,000 credits (3,610,399)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 149287 - Posted: 9 Mar 2021 | 14:31:43 UTC

Ok, thanks.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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

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