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Message boards : Proth Prime Search : Exact difference between PPS, PPSE and MEGA

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Profile BurProject donor
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Credit: 13,098,103
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321 LLR Gold: Earned 500,000 credits (538,216)Cullen LLR Gold: Earned 500,000 credits (624,600)ESP LLR Gold: Earned 500,000 credits (636,842)PPS LLR Gold: Earned 500,000 credits (837,557)PSP LLR Silver: Earned 100,000 credits (209,588)SR5 LLR Gold: Earned 500,000 credits (531,229)SGS LLR Amethyst: Earned 1,000,000 credits (1,022,026)TRP LLR Gold: Earned 500,000 credits (561,429)Woodall LLR Gold: Earned 500,000 credits (781,741)321 Sieve 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)GFN Amethyst: Earned 1,000,000 credits (1,722,477)PSA Bronze: Earned 10,000 credits (10,909)
Message 141520 - Posted: 8 Jul 2020 | 16:41:59 UTC

I'm quite sure this was answered somewhere, but I can't find it.

From the stats page it looks like all PPS and MEGA are searching the same k's and similar max values for n. Is the whole range from 0 < n < 3.xM sieved and then MEGA checks larger n while PPS check smaller ones?

What is the exact range of n and is it completely covered?

PPSE appears to seach larger k exclusively?

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Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de Primes321 LLR Gold: Earned 500,000 credits (663,646)Cullen LLR Gold: Earned 500,000 credits (507,205)ESP LLR Gold: Earned 500,000 credits (516,221)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (500,544)PPS LLR Amethyst: Earned 1,000,000 credits (1,180,833)PSP LLR Gold: Earned 500,000 credits (530,606)SoB LLR Gold: Earned 500,000 credits (859,020)SR5 LLR Gold: Earned 500,000 credits (501,196)SGS LLR Amethyst: Earned 1,000,000 credits (1,000,114)TRP LLR Gold: Earned 500,000 credits (631,674)Woodall LLR Gold: Earned 500,000 credits (508,734)321 Sieve Amethyst: Earned 1,000,000 credits (1,000,211)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,420)PPS Sieve Sapphire: Earned 20,000,000 credits (22,407,037)AP 26/27 Sapphire: Earned 20,000,000 credits (20,065,409)GFN Sapphire: Earned 20,000,000 credits (34,508,424)PSA Sapphire: Earned 20,000,000 credits (20,070,245)
Message 141527 - Posted: 8 Jul 2020 | 18:01:40 UTC - in response to Message 141520.

I'm quite sure this was answered somewhere, but I can't find it.

From the stats page it looks like all PPS and MEGA are searching the same k's and similar max values for n. Is the whole range from 0 < n < 3.xM sieved and then MEGA checks larger n while PPS check smaller ones?

What is the exact range of n and is it completely covered?

PPSE appears to seach larger k exclusively?

PPS is for odd k's in 4<k<1200. PPSE is for odd k's in 1200<k<10000. PPS-MEGA started searching with PPS k's but was moved to PPSE k's a little while back. Select k's are also being searched in the PPS-DIV subproject right now at higher n values. I'm 99% sure the search started at n=10k, but I don't have a source handy for that.

Sieving is complete for 0<n<6M and undergoing for 6M<n<9M. This is being done through the PPS-Sieve subproject.

The stats pages aren't ideal for this information since it doesn't show gaps between PPS/PPSE and MEGA.

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)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 Turquoise: Earned 5,000,000 credits (8,175,752)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 (104,534)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)AP 26/27 Bronze: Earned 10,000 credits (12,129)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 141534 - Posted: 8 Jul 2020 | 20:18:52 UTC - in response to Message 141527.

Well explained.

I believe in the old days, PPS (i.e. 4 < k < 1200) was searched in chunks in an uneven way such that small k were advanced further than large k. This makes sense in many ways, but is hard to manage. The lowest k values reached megaprime domain in PPS, while the other k were far from reaching megaprimes.

The MEGA project was created starting just over the megaprime level (except k that were past that). And the PPSE was created doing small n in 1200 < k < 10000 instead, is you said. A new philosophy was initiated at PPS to try to have a "straight" leading edge, where all k are at the same n simultaneously.

MEGA was later moved to 1200 < k < 10000 to have many new candidates "just over" 10^999999.

It was realized that the new PPS philosophy was bad for Fermat divisor progress (setting low k on halt for several years), and therefore the DIV project was created to focus on 4 < k < 50 (and initially a couple of other magical k values, but those have been abandoned now). It is often forgotten that for two special k, namely k=9 and k=27, we are only considering odd exponents n in DIV. The even n for k=9 must wait; the even n for k=27 have been singly checked, see next paragraph.

For completeness, the multipliers k = 3, k = 27, and k = 121 have special subprojects, namely 321 (here on BOINC) and 27/121 (PRPNet), and in them, both +1 and -1 forms are searched. In 27/121, the double check is left to DIV (27, odd n, +1 form) and PPS (other +1 forms).

/JeppeSN

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Credit: 17,941,086
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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)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 Turquoise: Earned 5,000,000 credits (8,175,752)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 (104,534)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)AP 26/27 Bronze: Earned 10,000 credits (12,129)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 141535 - Posted: 8 Jul 2020 | 20:26:58 UTC

It seems for k > 100, there is still a gap between PPS/PPSE leading edges (which are below the megaprime level) and MEGA. For 10 < k < 100, PPS has "caught up" on MEGA, and the gap has been closed. For 4 < k < 10, classical PPS was already over megaprime level before MEGA was created, and MEGA has never searched them, and never will. /JeppeSN

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Joined: 25 Feb 20
Posts: 223
ID: 1241833
Credit: 13,098,103
RAC: 135,292
321 LLR Gold: Earned 500,000 credits (538,216)Cullen LLR Gold: Earned 500,000 credits (624,600)ESP LLR Gold: Earned 500,000 credits (636,842)PPS LLR Gold: Earned 500,000 credits (837,557)PSP LLR Silver: Earned 100,000 credits (209,588)SR5 LLR Gold: Earned 500,000 credits (531,229)SGS LLR Amethyst: Earned 1,000,000 credits (1,022,026)TRP LLR Gold: Earned 500,000 credits (561,429)Woodall LLR Gold: Earned 500,000 credits (781,741)321 Sieve 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)GFN Amethyst: Earned 1,000,000 credits (1,722,477)PSA Bronze: Earned 10,000 credits (10,909)
Message 141588 - Posted: 10 Jul 2020 | 5:47:56 UTC

Thanks!

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Message boards : Proth Prime Search : Exact difference between PPS, PPSE and MEGA

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