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Message boards : Proth Prime Search : Naive question about 24M-digits PPS numbers

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Profile Luigi R.Project donor
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Found 1 prime in the 2020 Tour de Primes321 LLR Silver: Earned 100,000 credits (124,678)Cullen LLR Silver: Earned 100,000 credits (113,279)ESP LLR Silver: Earned 100,000 credits (124,346)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (132,569)PPS LLR Ruby: Earned 2,000,000 credits (3,241,820)PSP LLR Silver: Earned 100,000 credits (172,629)SoB LLR Amethyst: Earned 1,000,000 credits (1,343,981)SR5 LLR Gold: Earned 500,000 credits (831,103)SGS LLR Silver: Earned 100,000 credits (133,910)TRP LLR Silver: Earned 100,000 credits (112,374)Woodall LLR Silver: Earned 100,000 credits (100,235)321 Sieve Silver: Earned 100,000 credits (100,021)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (115,766)PPS Sieve Sapphire: Earned 20,000,000 credits (20,013,627)TRP Sieve (suspended) Silver: Earned 100,000 credits (108,608)AP 26/27 Turquoise: Earned 5,000,000 credits (5,021,406)GFN Turquoise: Earned 5,000,000 credits (6,385,570)PSA Gold: Earned 500,000 credits (661,014)
Message 137239 - Posted: 5 Feb 2020 | 10:14:29 UTC

Just curious. Is it theoretically possible to have a PPS-DYFL subproject (PPS - Do You Feel Lucky?) that searches, for instance, the range 1200<k<10000 and n>=82589926? Are there hardware/software limitations?
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Message 137242 - Posted: 5 Feb 2020 | 11:52:41 UTC - in response to Message 137239.

Too long for us to test. Using Yves' Proth2.0 ocl though it could be possible...?
Look at the SoB tasks which are at 32M. and then compare 32M to 82M and note there's a exponential increase in time as the exponent grows (hmm, pun).
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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 (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (9,594,179)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve 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 Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 137244 - Posted: 5 Feb 2020 | 11:54:14 UTC

If you were to go to such high exponents n, surely you would pick tiny k, like k = 3; 5; 7; etc.?

You could try to start LLR on one such candidate, like 3*2^82589933 + 1. I do not know if it will run. If it will, it will take a LONG time.

I suspect Yves's upcoming GPU Proth application will be unable to cope with such huge numbers.

/JeppeSN

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Message 137246 - Posted: 5 Feb 2020 | 12:27:15 UTC

Well, long run times don't shock me. Mersenne prime searchers are testing the 90-100M range.

Yeah, k could be chosen lower.
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Found 5 primes in the 2021 Tour de PrimesFound 5 mega primes in the 2021 Tour de PrimesThe "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 6 mega primesFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,624,591)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,008,485)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,252,256)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,911,985)321 Sieve Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)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 Jade: Earned 10,000,000 credits (10,118,303)GFN Emerald: Earned 50,000,000 credits (76,733,355)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 137247 - Posted: 5 Feb 2020 | 12:40:23 UTC

Can you? Sure. The question is why?

Obviously, any number of that size takes a long time to test. If the goal is specifically to find a world record prime, and you don't really care what kind of number you're testing, you would pick the type of number with the fastest test.

That's why GIMPS is searching Mersenne numbers.

The second fastest number to test are Generalized Fermat numbers. That's why we're searching GFN-DYFL.

Is there a reason to search Proth numbers of that size? If the goal is to find a world record prime, Generalized Fermat numbers are better.
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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 (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (9,594,179)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve 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 Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 137249 - Posted: 5 Feb 2020 | 12:51:41 UTC

Suppose you discovered a 3*2^n + 1 prime greater than all known Mersenne primes (world record prime). It would take an incredible amount of time to find out what ((x)G)F numbers it divided. /JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Silver: Earned 100,000 credits (124,678)Cullen LLR Silver: Earned 100,000 credits (113,279)ESP LLR Silver: Earned 100,000 credits (124,346)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (132,569)PPS LLR Ruby: Earned 2,000,000 credits (3,241,820)PSP LLR Silver: Earned 100,000 credits (172,629)SoB LLR Amethyst: Earned 1,000,000 credits (1,343,981)SR5 LLR Gold: Earned 500,000 credits (831,103)SGS LLR Silver: Earned 100,000 credits (133,910)TRP LLR Silver: Earned 100,000 credits (112,374)Woodall LLR Silver: Earned 100,000 credits (100,235)321 Sieve Silver: Earned 100,000 credits (100,021)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (115,766)PPS Sieve Sapphire: Earned 20,000,000 credits (20,013,627)TRP Sieve (suspended) Silver: Earned 100,000 credits (108,608)AP 26/27 Turquoise: Earned 5,000,000 credits (5,021,406)GFN Turquoise: Earned 5,000,000 credits (6,385,570)PSA Gold: Earned 500,000 credits (661,014)
Message 137253 - Posted: 5 Feb 2020 | 13:45:44 UTC - in response to Message 137247.
Last modified: 5 Feb 2020 | 13:46:55 UTC

Ok, Micheal's answer is very clear. Thanks!

I will try to understand how much Proth numbers primality tests are slower.

If I search for a world record prime, I would care that my prime will be beautiful/elegant.
I like primorial/factorial primes because only 1 number (and +/- 1) is needed to represent them. :)
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Message 137272 - Posted: 5 Feb 2020 | 20:29:32 UTC - in response to Message 137253.

I like primorial/factorial primes because only 1 number (and +/- 1) is needed to represent them. :)


Both primorial and factorial searches are due. It has been nearly 8 years since the last primorial prime and 6.5 years since the last factorial prime.

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Discovered 4 mega primesEliminated 1 conjecture "k"Found 3 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 5 primes in the 2019 Tour de PrimesFound 6 primes in the 2020 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (8,774,878)Cullen LLR Turquoise: Earned 5,000,000 credits (5,903,451)ESP LLR Turquoise: Earned 5,000,000 credits (6,454,573)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,122,074)PPS LLR Emerald: Earned 50,000,000 credits (83,377,417)PSP LLR Jade: Earned 10,000,000 credits (15,223,714)SoB LLR Jade: Earned 10,000,000 credits (17,319,914)SR5 LLR Sapphire: Earned 20,000,000 credits (23,996,561)SGS LLR Turquoise: Earned 5,000,000 credits (7,342,780)TPS LLR (retired) Bronze: Earned 10,000 credits (34,130)TRP LLR Jade: Earned 10,000,000 credits (19,866,589)Woodall LLR Turquoise: Earned 5,000,000 credits (8,171,820)321 Sieve Sapphire: Earned 20,000,000 credits (20,236,219)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,383,853)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,626,419)PPS Sieve Emerald: Earned 50,000,000 credits (76,969,144)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,293,882)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,012,757)AP 26/27 Sapphire: Earned 20,000,000 credits (21,918,894)GFN Emerald: Earned 50,000,000 credits (76,466,089)PSA Ruby: Earned 2,000,000 credits (2,939,755)
Message 137277 - Posted: 5 Feb 2020 | 21:08:06 UTC - in response to Message 137244.

You could try to start LLR on one such candidate, like 3*2^82589933 + 1. I do not know if it will run. If it will, it will take a LONG time.

Just tried it with LLR, before moving to using Prime95 built in benchmark function with a 4608k FFT reported by LLR as required. Timings were similar.

As a rough estimate, it'll take 5.5 to 6 days on a 6 core Coffee Lake running at 4 GHz with 3200 dual channel, single rank ram. This would likely go down with faster ram, more so than faster CPU.

A 7920X with 12 cores at 2.9 GHz (turbo disabled), quad channel 2DPC 3000 ram, could do it in under 2 days. I'd guess it is still more ram bandwidth limited than CPU limited.

Intel CPUs don't have the cache so it'll be ram bandwidth limited. Zen 2 has more cache, but because it is not unified it doesn't fully unleash its core potential, although still gives some boost relative to the ram bandwidth considered alone.

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Found 3 primes in the 2020 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,063,954)Cullen LLR Amethyst: Earned 1,000,000 credits (1,328,304)ESP LLR Turquoise: Earned 5,000,000 credits (8,170,793)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,319,313)PPS LLR Jade: Earned 10,000,000 credits (14,623,895)PSP LLR Ruby: Earned 2,000,000 credits (2,012,651)SoB LLR Amethyst: Earned 1,000,000 credits (1,064,898)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Amethyst: Earned 1,000,000 credits (1,320,684)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Amethyst: Earned 1,000,000 credits (1,492,539)321 Sieve Turquoise: Earned 5,000,000 credits (5,440,175)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Emerald: Earned 50,000,000 credits (50,200,870)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Turquoise: Earned 5,000,000 credits (5,442,696)GFN Sapphire: Earned 20,000,000 credits (33,288,606)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 137300 - Posted: 6 Feb 2020 | 5:10:07 UTC

I suspect Yves's upcoming GPU Proth application will be unable to cope with such huge numbers.

Where is this being discussed? What has changed in the last couple of years that makes LLR on GPU reasonable now?
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Message 137302 - Posted: 6 Feb 2020 | 5:48:49 UTC - in response to Message 137300.

I suspect Yves's upcoming GPU Proth application will be unable to cope with such huge numbers.

Where is this being discussed? What has changed in the last couple of years that makes LLR on GPU reasonable now?

Yves has told us about it on the PG Discord server. There's also some discussion on the Mersenne forum here.

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Message 137308 - Posted: 6 Feb 2020 | 9:46:14 UTC - in response to Message 137300.
Last modified: 6 Feb 2020 | 12:26:21 UTC

Where is this being discussed? What has changed in the last couple of years that makes LLR on GPU reasonable now?

This is not LLR. LLR is based on complex FFT and 64-bit FP numbers. That's efficient on CPU because of fast AVX or AVX-512 units. But GPUs have no fast 64-bit FP units (except expensive Tesla with GP100 or GV100).
proth20 is based on a Number Theoretic Transform. A good point with this method is that the primality proof is deterministic.

We can test a 24M-digit Proth number with proth20 but the size of the transform is 2^23. With genefer, the size of the transform of a 24M-digit generalized Fermat number is 2^22. genefer is twice as fast. The reason for this is that the transform of genefer (which is not based on FFTs) computes P(x)^2 (mod x^{2^n} + 1). We can apply the same method to cyclotomic polynomials as x^{2^n} - x^{2^{n-1}} + 1 (Phi(3, -123447^524288) was found by this method). But Proth numbers are not "cyclotomic numbers" then we have to compute P(x)^2 and reduce the result modulo k·2^n+1. Is it possible to compute a sort of IBDWT with integers and a fast deterministic Proth test? ... I haven't found it.

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Discovered 2 mega primesFound 1 prime in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,477,467)Cullen LLR Gold: Earned 500,000 credits (776,297)ESP LLR Ruby: Earned 2,000,000 credits (3,120,351)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,056,207)PPS LLR Sapphire: Earned 20,000,000 credits (21,475,108)PSP LLR Turquoise: Earned 5,000,000 credits (5,027,818)SoB LLR Sapphire: Earned 20,000,000 credits (25,095,209)SR5 LLR Turquoise: Earned 5,000,000 credits (6,110,877)SGS LLR Ruby: Earned 2,000,000 credits (3,477,744)TRP LLR Turquoise: Earned 5,000,000 credits (7,025,303)Woodall LLR Amethyst: Earned 1,000,000 credits (1,693,614)321 Sieve Emerald: Earned 50,000,000 credits (50,256,050)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,571,178)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,009,610)PPS Sieve Double Silver: Earned 200,000,000 credits (316,075,694)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,165,888)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,071,454)AP 26/27 Turquoise: Earned 5,000,000 credits (6,616,128)GFN Emerald: Earned 50,000,000 credits (53,042,140)PSA Double Bronze: Earned 100,000,000 credits (102,762,384)
Message 137317 - Posted: 6 Feb 2020 | 13:56:06 UTC - in response to Message 137308.

Is it possible to compute a sort of IBDWT with integers and a fast deterministic Proth test? ... I haven't found it.

How far does this all integer IBDWT (GitHub) get you toward that goal?

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Message 137329 - Posted: 6 Feb 2020 | 17:11:10 UTC - in response to Message 137317.

Is it possible to compute a sort of IBDWT with integers and a fast deterministic Proth test? ... I haven't found it.

How far does this all integer IBDWT (GitHub) get you toward that goal?

I didn't know that code (I prefer the C version ioccc2012/mersenne.c).
Very interesting, now the idea is to mix it with Colin Percival's multiplication Rapid multiplication modulo the sum and difference of highly composite numbers.
Some good work for the future... :o)

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Message boards : Proth Prime Search : Naive question about 24M-digits PPS numbers

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