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Message boards : Proth Prime Search : Status and strategy for small k values

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Profile JeppeSNProject donor
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321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (184,660)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 122649 - Posted: 18 Nov 2018 | 20:56:37 UTC

I was trying to get an overview of the status and activity for Proth prime search with small k values.

I find the small k most interesting because (1) they are more "beautiful" because they are {a more round number} plus one, and (2) they are more often divisors of Fermat numbers of (extended) generalized Fermat numbers.

k=3:

This seems to be well handled by 321 search (the plus half of it). See /stats_321_llr.php

k in { 5, 7, 9 }:

There is no "521 search" (although 521 is a nice name). Who votes for one?

These multipliers are not in the MEGA stats page /stats_mega_llr.php, but it appears the "ordinary" PPS project goes beyond the megaprime level for these k, see /stats_pps_llr.php. They stand at 6M, 6M, and 4M for the k values for resp. 5, 7, and 9.

Is it true that these will be handled by PPS (not MEGA)? When will these small k be prioritized again?

k in { 11, 13 }:

On the ordinary PPS stats page, these stop at the megaprime level, but 11 and 13 are included in the MEGA stats page, /stats_mega_llr.php. They stand at k equal to 3.6M there.

However, on http://www.prothsearch.com/riesel1.html, under 11 and 13, we see 5.5M and 5M, respectively, in the square brackets. Is someone outside PrimeGrid taking the lead here? That would be a shame.

Will k=11 and k=13 be run under MEGA in the future? When will they become active again (is there a plan)?

k in { 15, ..., 99 }:

On PPS, these currently stand at the megaprime threshold. On the MEGA stats page, these k values are absent? A few k limit values on prothsearch.com are higher than the megaprime limit (which is about k=3.32M).

For some of these k values, on Caldwell's Top 5000, the record for that k is discovered by Serge Batalov outside PrimeGrid.

Will k between 15 and 99 be run on the MEGA project in the future?

k in { 101, ... }:

Here we have a gap between PPS (which is still below the megaprime level) and MEGA. It looks like both projects cover these exponents (up to 1200, and from there covered by PPSE).

When k>100, the primes are less spectacular (my opinion), and less like to divide Fermat numbers (unsurprising empirical fact).

/JeppeSN

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Credit: 11,356,014
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321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (184,660)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 122987 - Posted: 28 Nov 2018 | 22:19:15 UTC

My post did not really lead to any answers, comments or corrections.

Does anyone know (or forecast) when Proth numbers (other than 321) with k less than 100 will be run again?

/JeppeSN

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Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,380,810)Cullen LLR Ruby: Earned 2,000,000 credits (4,977,206)ESP LLR Turquoise: Earned 5,000,000 credits (5,064,082)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,758,820)PPS LLR Ruby: Earned 2,000,000 credits (3,014,081)PSP LLR Turquoise: Earned 5,000,000 credits (5,013,650)SoB LLR Sapphire: Earned 20,000,000 credits (42,406,112)SR5 LLR Jade: Earned 10,000,000 credits (10,987,079)SGS LLR Ruby: Earned 2,000,000 credits (2,069,865)TRP LLR Ruby: Earned 2,000,000 credits (2,150,717)Woodall LLR Ruby: Earned 2,000,000 credits (3,083,808)321 Sieve Turquoise: Earned 5,000,000 credits (6,000,049)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,002,919)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,005,451)PPS Sieve Emerald: Earned 50,000,000 credits (50,809,179)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,341,676)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,804)AP 26/27 Jade: Earned 10,000,000 credits (10,742,251)GFN Sapphire: Earned 20,000,000 credits (31,496,305)PSA Double Gold: Earned 500,000,000 credits (644,180,573)
Message 122998 - Posted: 29 Nov 2018 | 0:59:06 UTC
Last modified: 29 Nov 2018 | 1:05:03 UTC

Once upon a time, when Lennart was in charge of such things, the low k values were tested to relatively high n levels. k=(5,7) were tested to n=6M, k=9 was tested to n=4M. Every other odd k < 1200 was either already tested or is currently loaded to n=3.6M. So k=11-1199 will start being tested in MEGA at n=3.6M+ the next time we need to load work there. It'll be a couple of years before we get to k=9 and I suspect ten or more years before k=5 and k=7 are back in the mix.

PPS LLR is loaded with k=301-1199 up to n=2.7M right now. k from 101-299 were done to n=3.05M, so at that point k=101-299 will start being tested again. They will all stop at n=3.322M where PPS MEGA started. It's uncertain what happens then. We could continue PPS MEGA using the PPSE k values of 1201-9999 or discontinue PPS MEGA altogether. It's not a choice that needs to be made right now.

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Message boards : Proth Prime Search : Status and strategy for small k values

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