PrimeGrid
Please visit donation page to help the project cover running costs for this month

Toggle Menu

Join PrimeGrid

Returning Participants

Community

Leader Boards

Results

Other

drummers-lowrise

Advanced search

Message boards : General discussion : Extended generalized Fermat prime?

Author Message
Profile BurProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Feb 20
Posts: 411
ID: 1241833
Credit: 192,187,621
RAC: 989,353
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,426,937)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,703)TRP LLR Amethyst: Earned 1,000,000 credits (1,055,045)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (165,048,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 146647 - Posted: 14 Dec 2020 | 18:13:38 UTC

I read in Riesel's 1994 book "Prime Numbers and Computer Methods for Factorization" that he tried finding primes of that form but to no avail. Even today there is no such catergory at Caldwell's prime list, so I assume none are known?

Are there any conjectures there might not be any at all?
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Ravi Fernando
Project administrator
Volunteer tester
Project scientist
Send message
Joined: 21 Mar 19
Posts: 162
ID: 1108183
Credit: 9,578,782
RAC: 5,699
321 LLR Gold: Earned 500,000 credits (575,511)Cullen LLR Bronze: Earned 10,000 credits (82,217)ESP LLR Bronze: Earned 10,000 credits (16,570)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (12,551)PPS LLR Ruby: Earned 2,000,000 credits (2,820,433)PSP LLR Bronze: Earned 10,000 credits (26,371)SoB LLR Silver: Earned 100,000 credits (258,849)SR5 LLR Bronze: Earned 10,000 credits (59,499)SGS LLR Silver: Earned 100,000 credits (148,878)TRP LLR Silver: Earned 100,000 credits (195,905)Woodall LLR Bronze: Earned 10,000 credits (40,424)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,001,667)AP 26/27 Bronze: Earned 10,000 credits (72,774)WW Bronze: Earned 10,000 credits (12,000)GFN Silver: Earned 100,000 credits (248,769)
Message 146649 - Posted: 14 Dec 2020 | 18:40:22 UTC - in response to Message 146647.

Not sure where you're getting the idea that none of them are known. There are plenty of small ones--see e.g. the table with "a" and "b" columns a little ways below here. But there are no proven xGFN primes that are large enough for Caldwell's list, simply because it's usually not feasible to factor p+1 or p-1. For example, the two PRPs of the form a^2^16 + b^2^16 listed here cannot be proved prime with current methods, even though they're pretty small by T5K standards.

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1504
ID: 306875
Credit: 34,174,782
RAC: 9,496
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 (12,277,293)PSP LLR Silver: Earned 100,000 credits (212,242)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)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 146654 - Posted: 14 Dec 2020 | 21:41:19 UTC

Also try the PRP Top search a^x+b^x. /JeppeSN

Profile BurProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Feb 20
Posts: 411
ID: 1241833
Credit: 192,187,621
RAC: 989,353
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,426,937)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,703)TRP LLR Amethyst: Earned 1,000,000 credits (1,055,045)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (165,048,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 146682 - Posted: 15 Dec 2020 | 18:46:02 UTC - in response to Message 146654.
Last modified: 15 Dec 2020 | 18:47:27 UTC

Thanks, that's a bit embarassing. I didn't get the division by gcd(a+b,2) in the wikipedia table. But apparently that just means: if a+b is even, the sum will be divided by 2, same as the "half generalized Fermats"?

Regarding Caldwell's, I thought he included special types of primes irregardless of their size, as long as they are the top 20 largest known ones. For example Wagstaff primes. The smallest have only about 1000 digits. That should be achievable for xGFs.
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1504
ID: 306875
Credit: 34,174,782
RAC: 9,496
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 (12,277,293)PSP LLR Silver: Earned 100,000 credits (212,242)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)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 146689 - Posted: 15 Dec 2020 | 20:25:56 UTC - in response to Message 146682.

Yeah, if a and b are both odd, divide by 2. PRP Top search: http://www.primenumbers.net/prptop/searchform.php?form=%28a%5Ex%2Bb%5Ex%29%2F2 (Kellen and me). /JeppeSN

Profile BurProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Feb 20
Posts: 411
ID: 1241833
Credit: 192,187,621
RAC: 989,353
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,426,937)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,703)TRP LLR Amethyst: Earned 1,000,000 credits (1,055,045)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (165,048,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 146709 - Posted: 16 Dec 2020 | 18:49:59 UTC - in response to Message 146689.

So these would need to be proven via ECPP or APR-CL? How long does a proof approximately take, compared to LLR? Since it apparently wasn't undertaken by you, I guess: very long?

Is it even possible with current software? Primo doesn't seem to support candidates larger than 50 000 digits.

On the other hand this comparison from 2014 makes these methods look relatively fast. Maybe a few days for 100 000 digits. Or do things change dramatically when the number of digits increases further?
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Profile GellyProject donor
Volunteer tester
Avatar
Send message
Joined: 13 Nov 16
Posts: 46
ID: 468732
Credit: 1,967,372,105
RAC: 784,701
Discovered 2 mega primesFound 1 prime in the 2018 Tour de PrimesFound 2 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Bronze: Earned 10,000 credits (38,954)ESP LLR Gold: Earned 500,000 credits (942,185)PPS LLR Double Silver: Earned 200,000,000 credits (284,953,062)PSP LLR Silver: Earned 100,000 credits (489,641)SoB LLR Jade: Earned 10,000,000 credits (12,960,428)SR5 LLR Jade: Earned 10,000,000 credits (10,694,695)SGS LLR Gold: Earned 500,000 credits (563,819)TRP LLR Jade: Earned 10,000,000 credits (13,032,763)321 Sieve (suspended) Silver: Earned 100,000 credits (395,205)PPS Sieve Double Silver: Earned 200,000,000 credits (229,814,554)TRP Sieve (suspended) Gold: Earned 500,000 credits (669,191)AP 26/27 Sapphire: Earned 20,000,000 credits (25,547,717)WW Double Amethyst: Earned 1,000,000,000 credits (1,304,232,000)GFN Emerald: Earned 50,000,000 credits (80,008,560)PSA Ruby: Earned 2,000,000 credits (3,025,234)
Message 146710 - Posted: 16 Dec 2020 | 19:06:42 UTC - in response to Message 146709.

ECPP is achingly slow. There is a reason the official version of primo only goes up to 50k decimal digits. The current record, 40k digits, was set by Paul Underwood on 48 thread hardware that took more than a year and was nothing to sneeze at. My 3970x threadripper, a 32 core, 64 thread beast, takes two weeks to months to prove candidates in the 20k digit range.

As a rule of thumb, when you double the amount of digits in the number to be tested, the time it takes goes up 16 to 32 times, depending on how lucky you are. It will likely be years before Paul proves the next big step in ECPP (the smallest unproven repunit, 49k digits), and I'm sure he either got a 3990x (64 cores!) or maybe even doshed out on EPYC.

100k digits, on current hardware with current methods, would take decades.

Profile BurProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Feb 20
Posts: 411
ID: 1241833
Credit: 192,187,621
RAC: 989,353
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,426,937)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,703)TRP LLR Amethyst: Earned 1,000,000 credits (1,055,045)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (165,048,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 147020 - Posted: 24 Dec 2020 | 7:26:54 UTC

Ok, thanks. One can loose the feeling for how large these 20k+ digits numbers actually are, because their primality can be proven so easily.

Projects like WW help a bit since we're suddenly dealing with a mere 18 digits and already things take a while.
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1504
ID: 306875
Credit: 34,174,782
RAC: 9,496
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 (12,277,293)PSP LLR Silver: Earned 100,000 credits (212,242)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)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 147025 - Posted: 24 Dec 2020 | 10:33:27 UTC - in response to Message 147020.

Projects like WW help a bit since we're suddenly dealing with a mere 18 digits and already things take a while.


However, in WW you start with a range of one trillion (10^12) numbers. Then you find out which of those numbers are primes and which are not; there are going to billions of primes. Then for each of those billions of primes, you check if they have the Wieferich property or the Wall-Sun-Sun property.

So this is in no way comparable to testing one specific 20'000-digit candidate number for primality.

/JeppeSN

Post to thread

Message boards : General discussion : Extended generalized Fermat prime?

[Return to PrimeGrid main page]
DNS Powered by DNSEXIT.COM
Copyright © 2005 - 2021 Rytis Slatkevičius (contact) and PrimeGrid community. Server load 3.46, 3.11, 2.99
Generated 18 Jun 2021 | 12:15:08 UTC