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Message boards : General discussion : What PrimeGrid prime numbers are used for?

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EMYArg
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Message 105408 - Posted: 26 Feb 2017 | 21:56:37 UTC

Hello everyone

I leave here a question, surely other people have already asked the same thing, forum administrators can delete my question if they wish.

Question: Can anyone tell me what PrimeGrid prime numbers are used for?

Thank you.

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Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Ruby: Earned 2,000,000 credits (2,982,482)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,073,792)TRP LLR Silver: Earned 100,000 credits (122,712)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (10,561,511)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,575,874)GFN Sapphire: Earned 20,000,000 credits (23,152,487)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 105410 - Posted: 26 Feb 2017 | 22:05:09 UTC - in response to Message 105408.

Except fact, that is very rare, for nothing :)
____________
93*10^1029523-1 REPDIGIT MEGA PRIME :) :) :)
57*2^3339932-1 MEGA PRIME :)
10994460^131072+1 GENERALIZED FERMAT :)
31*332^367560+1 CRUS PRIME :)
Proud member of team Aggie The Pew. Go Aggie!

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Message 105416 - Posted: 26 Feb 2017 | 23:51:41 UTC - in response to Message 105408.
Last modified: 26 Feb 2017 | 23:57:36 UTC

Hello everyone

I leave here a question, surely other people have already asked the same thing, forum administrators can delete my question if they wish.

Question: Can anyone tell me what PrimeGrid prime numbers are used for?

Thank you.

On the conjecture projects (ESP, PSP, SoB, SR5, TRP) they help to prove the conjecture. For other projects, they're just relatively large prime numbers with no use in particular. We do check all primes of the form k*2^n+1 where k<> 1 to see if they're Fermat divisors, but someone else would have to explain why those are useful.

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Message 105431 - Posted: 27 Feb 2017 | 15:20:37 UTC - in response to Message 105416.

Also, projects such as the smaller Generalized Fermat Number (GFN) searches may help test whether models on the expected frequency of primes among such numbers seem to be corroborated by numerical evidence or not. However, by the nature of it, no rigorous proof or refutation of statements about the asymptotic behavior can come out of this. Only indications. /JeppeSN

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Found 1 prime in the 2018 Tour de Primes321 LLR Gold: Earned 500,000 credits (860,905)Cullen LLR Gold: Earned 500,000 credits (506,431)ESP LLR Gold: Earned 500,000 credits (818,638)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (513,349)PPS LLR Ruby: Earned 2,000,000 credits (2,605,836)PSP LLR Gold: Earned 500,000 credits (555,892)SoB LLR Ruby: Earned 2,000,000 credits (2,296,322)SR5 LLR Ruby: Earned 2,000,000 credits (3,660,196)SGS LLR Amethyst: Earned 1,000,000 credits (1,410,704)TRP LLR Gold: Earned 500,000 credits (765,119)Woodall LLR Gold: Earned 500,000 credits (532,512)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,321,574)PPS Sieve Sapphire: Earned 20,000,000 credits (21,786,773)TRP Sieve (suspended) Gold: Earned 500,000 credits (528,024)AP 26/27 Jade: Earned 10,000,000 credits (10,220,704)GFN Sapphire: Earned 20,000,000 credits (48,145,047)PSA Sapphire: Earned 20,000,000 credits (34,628,282)
Message 105434 - Posted: 27 Feb 2017 | 18:04:32 UTC - in response to Message 105431.

I may be wrong but very large prime numbers are also used for encryption.

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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,135,461)PPS LLR Ruby: Earned 2,000,000 credits (2,768,012)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (31,541,403)SR5 LLR Turquoise: Earned 5,000,000 credits (7,691,131)SGS LLR Ruby: Earned 2,000,000 credits (2,011,264)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,176,414)321 Sieve Ruby: Earned 2,000,000 credits (2,816,982)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (62,362,748)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 105436 - Posted: 27 Feb 2017 | 18:10:29 UTC - in response to Message 105434.

I may be wrong but very large prime numbers are also used for encryption.


That is true, but "large" is a very subjective adjective.

The prime numbers used in encryption are positively miniscule compared to the prime numbers we search for here.

Where PrimeGrid's work helps with things like encryption is the techniques than theorems that enable the searches for the really large primes can then be used to easily find the small primes used in encryption technologies.
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Message boards : General discussion : What PrimeGrid prime numbers are used for?

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