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Message boards : The Riesel Problem : K = 192971 prime found by Propper

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MargusProject donor
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Discovered 2 mega primesFound 2 primes in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,012,291)Cullen LLR Turquoise: Earned 5,000,000 credits (5,020,355)ESP LLR Turquoise: Earned 5,000,000 credits (5,186,692)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,057,386)PPS LLR Sapphire: Earned 20,000,000 credits (37,723,941)PSP LLR Turquoise: Earned 5,000,000 credits (5,357,907)SoB LLR Turquoise: Earned 5,000,000 credits (6,356,903)SR5 LLR Jade: Earned 10,000,000 credits (11,099,073)SGS LLR Turquoise: Earned 5,000,000 credits (5,135,397)TRP LLR Turquoise: Earned 5,000,000 credits (7,490,542)Woodall LLR Turquoise: Earned 5,000,000 credits (5,014,650)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,001,504)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,203,942)PPS Sieve Emerald: Earned 50,000,000 credits (55,843,986)AP 26/27 Sapphire: Earned 20,000,000 credits (22,907,638)GFN Sapphire: Earned 20,000,000 credits (33,946,060)WW Double Bronze: Earned 100,000,000 credits (104,524,000)PSA Emerald: Earned 50,000,000 credits (62,438,463)
Message 149210 - Posted: 7 Mar 2021 | 21:15:52 UTC

192971 · 2^14773498 - 1

Michael Millerick
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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,842,941)PPS LLR Jade: Earned 10,000,000 credits (19,232,686)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) 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 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (71,540,635)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 149211 - Posted: 7 Mar 2021 | 21:32:59 UTC

Hopefully we can get residues for these discoveries at some point to speed up the double checking of the work he is doing.
____________

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Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,011,570)Cullen LLR Jade: Earned 10,000,000 credits (10,009,374)ESP LLR Jade: Earned 10,000,000 credits (10,009,221)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (10,012,217)PPS LLR Jade: Earned 10,000,000 credits (16,277,057)PSP LLR Jade: Earned 10,000,000 credits (10,044,081)SoB LLR Jade: Earned 10,000,000 credits (10,064,750)SR5 LLR Jade: Earned 10,000,000 credits (10,002,051)SGS LLR Jade: Earned 10,000,000 credits (10,001,295)TRP LLR Jade: Earned 10,000,000 credits (10,002,411)Woodall LLR Jade: Earned 10,000,000 credits (10,013,921)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,004,228)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,047,667)PPS Sieve Sapphire: Earned 20,000,000 credits (20,866,490)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,043,271)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,015,177)AP 26/27 Sapphire: Earned 20,000,000 credits (20,045,194)GFN Emerald: Earned 50,000,000 credits (55,355,287)WW Sapphire: Earned 20,000,000 credits (20,160,000)PSA Double Silver: Earned 200,000,000 credits (200,301,443)
Message 149219 - Posted: 8 Mar 2021 | 9:22:55 UTC - in response to Message 149211.

Hopefully we can get residues for these discoveries at some point to speed up the double checking of the work he is doing.


With LLR2, we don't need these residues anymore. We're doing one LLR2 test anyway. With known residue, the system in most cases can skip certificate, but it'll save only a certificate - 1% of work. Not much difference.

Finding a prime at least allows to eliminate k, although this k remains in "half-tested" state (status of area between our leading edge and Propper's prime remains unclear). In most worst scenario, when Propper tested an overlapped range and found nothing, it becomes just a 100% waste of computing resources because we cannot trust his results (nor double-checked nor LLR2-certifitied) and have to do our one LLR2 test anyway - in exactly same way like we did without Propper.

It's really pity that so much computing power is wasted. May be Ryan is just unaware of new LLR2 capabilities, especially, which can be most important for him, no more need for double-checkers - users having extreme computing power can now run "one man projects" with uninterrupted flow of tasks.


As for current prime, we decided to concentrate on conjecture itself and stop testing of both this k and his previous discovery, although area between our leading edge and his primes should be considered untested, and other primes can exist in this "grey zone".

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Message 149230 - Posted: 8 Mar 2021 | 14:39:02 UTC

Note that the computers of a large computing center may not be connected to the Internet for security reasons. Then you can't run PrimeGrid on them.

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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 (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,158,985)PSP LLR Silver: Earned 100,000 credits (428,457)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)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 149264 - Posted: 8 Mar 2021 | 23:54:27 UTC - in response to Message 149219.

May be Ryan is just unaware of new LLR2 capabilities, especially, which can be most important for him, no more need for double-checkers

I have wondered about that. The user Ryan Propper has existed here on PrimeGrid since 2007. But all the primes he has, are LLR2 primes (oldest one is from December).

While I do not know what he is aware, he has started to be credited as finder of PrimeGrid primes after LLR2 was introduced.

/JeppeSN

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Discovered 6 mega primesFound 1 prime in the 2021 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (23,075,144)Cullen LLR Sapphire: Earned 20,000,000 credits (43,411,077)ESP LLR Sapphire: Earned 20,000,000 credits (36,726,273)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (53,752,580)PPS LLR Emerald: Earned 50,000,000 credits (98,765,353)PSP LLR Emerald: Earned 50,000,000 credits (73,430,962)SoB LLR Double Bronze: Earned 100,000,000 credits (119,437,096)SR5 LLR Silver: Earned 100,000 credits (123,989)SGS LLR Amethyst: Earned 1,000,000 credits (1,197,965)TRP LLR Sapphire: Earned 20,000,000 credits (22,928,401)Woodall LLR Emerald: Earned 50,000,000 credits (52,155,683)321 Sieve (suspended) Silver: Earned 100,000 credits (153,081)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (938,164)PPS Sieve Jade: Earned 10,000,000 credits (12,300,779)GFN Double Ruby: Earned 2,000,000,000 credits (3,756,216,532)PSA Sapphire: Earned 20,000,000 credits (28,816,540)
Message 149296 - Posted: 10 Mar 2021 | 6:10:51 UTC

Let me try to clear a few things up, though I don't normally post here.

I do have a few personal machines running BOINC. I also have access to another cluster of machines, which aren't directly connected to the Internet. On these machines, I started doing some solo hunting of Riesel primes. I am explicitly searching 12e6 <= n <= 15e6. Unless I'm misunderstanding https://www.primegrid.com/stats_trp_llr.php this range should not conflict with Primegrid - now or for a while?

I don't particularly care about PrimeGrid credit, or T5K credit, or whatever. My main goal is to find primes that move the overall state of the Riesel problem forward. To that end, I undertook a solo search for some (k, n) ranges that I believed PrimeGrid was not actively investigating.

Hope that helps clear some things up.

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Found 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,133,351)Cullen LLR Turquoise: Earned 5,000,000 credits (5,420,696)ESP LLR Jade: Earned 10,000,000 credits (10,374,888)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,954,535)PPS LLR Sapphire: Earned 20,000,000 credits (22,501,783)PSP LLR Jade: Earned 10,000,000 credits (13,668,814)SoB LLR Turquoise: Earned 5,000,000 credits (6,446,373)SR5 LLR Ruby: Earned 2,000,000 credits (2,280,539)SGS LLR Amethyst: Earned 1,000,000 credits (1,028,652)TRP LLR Sapphire: Earned 20,000,000 credits (20,105,460)Woodall LLR Turquoise: Earned 5,000,000 credits (5,263,886)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (27,356,392)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (11,609,366)PPS Sieve Emerald: Earned 50,000,000 credits (99,457,984)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (128,472)TRP Sieve (suspended) Gold: Earned 500,000 credits (631,827)AP 26/27 Emerald: Earned 50,000,000 credits (50,218,103)GFN Emerald: Earned 50,000,000 credits (73,724,167)WW Amethyst: Earned 1,000,000 credits (1,848,000)PSA Bronze: Earned 10,000 credits (15,807)
Message 149300 - Posted: 10 Mar 2021 | 11:26:04 UTC - in response to Message 149296.

Not speaking for the project - don't know any "official" stance - but just from what I've seen/read I think the only issue is communication. Nobody likes duplicating someone else's work unnecessarily. Nobody "owns" a range to search, but there are sites that try to keep track of who is doing what. You have a HUGE amount of resources, and constantly DO advance the "art" - I'm both envious and impressed! The conflict arises when there's a surprise, when a prime is found in an area nobody realized was being searched by someone else. Then the question is "how sure are we that everything UP to that point was searched and double-checked, so we can safely skip it."

If there truly are no primes in some range, yet it has to be re-searched to be "sure", then it's a whole lot of CPU time used up with no new finds to reward the double-checkers. If it's not possible to provide sieve data or residues to other groups, that's understandable - and PG (or whoever) can decide to skip a range once you've posted a prime if they so decide - there's just a worry that work CURRENTLY being done might be being duplicated elsewhere without knowing it.

Knowing more about what you're doing and how would relieve a lot of minds. You have no obligation to speak at ALL of course - there's just both curiosity about what/how you're accomplishing so much, and concern about possible wasted effort. While some only care about the credits, others are actively seeking primes and will choose subprojects where they have a better chance of being the original finder.

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Found 1 prime in the 2018 Tour de Primes321 LLR Gold: Earned 500,000 credits (506,942)Cullen LLR Gold: Earned 500,000 credits (500,523)ESP LLR Gold: Earned 500,000 credits (655,642)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (539,100)PPS LLR Gold: Earned 500,000 credits (688,232)PSP LLR Gold: Earned 500,000 credits (561,629)SoB LLR Ruby: Earned 2,000,000 credits (3,659,676)SR5 LLR Gold: Earned 500,000 credits (505,810)SGS LLR Gold: Earned 500,000 credits (506,024)TRP LLR Gold: Earned 500,000 credits (963,625)Woodall LLR Gold: Earned 500,000 credits (506,044)321 Sieve (suspended) Gold: Earned 500,000 credits (511,694)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (549,916)PPS Sieve Gold: Earned 500,000 credits (701,168)AP 26/27 Gold: Earned 500,000 credits (525,590)GFN Jade: Earned 10,000,000 credits (10,762,872)WW Gold: Earned 500,000 credits (500,000)PSA Gold: Earned 500,000 credits (525,639)
Message 149302 - Posted: 10 Mar 2021 | 12:19:46 UTC
Last modified: 10 Mar 2021 | 12:41:24 UTC

Unless I'm misunderstanding https://www.primegrid.com/stats_trp_llr.php this range should not conflict with Primegrid - now or for a while?

For a while, yes.

PG has TRP k's fully sieved to n=50M according to this old post. The stats page shows the candidates currently "loaded" into the system and more are loaded from the sieve file periodically. Unless something happens, PG plans (as far as I'm aware) are to search each k until a prime is found or to the end of the sieve file (50M). This is, of course, a 10+ years plan.

EDIT: I'm pretty sure, if there is outside interest to run some of the K's externally with large resources and not have PG do work on them, PG admins could agree to some sort of arrangements of this kind.

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321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Amethyst: Earned 1,000,000 credits (1,976,771)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,073,355)AP 26/27 Ruby: Earned 2,000,000 credits (4,435,171)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 149311 - Posted: 10 Mar 2021 | 18:27:15 UTC - in response to Message 149302.

EDIT: I'm pretty sure, if there is outside interest to run some of the K's externally with large resources and not have PG do work on them, PG admins could agree to some sort of arrangements of this kind.
Maybe I get you wrong, but this sounds like PG has to agree on such a thing. We/they don't. Anyone has the same right to work on the Riesel Problem as we do.

Communication would be nice though. If someone announces to the rest of prime hunter community they will search a certain range, no one else has to do it.


Besides, I wonder why Ryan didn't pick the Sierpinski problem. Going after n = 40,000,000 and up would have really helped and been a challenge for a high-powered cluster.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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321 LLR Silver: Earned 100,000 credits (258,442)Cullen LLR Silver: Earned 100,000 credits (181,773)ESP LLR Silver: Earned 100,000 credits (239,556)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (199,718)PPS LLR Silver: Earned 100,000 credits (357,575)PSP LLR Silver: Earned 100,000 credits (321,756)SoB LLR Turquoise: Earned 5,000,000 credits (5,949,528)SR5 LLR Silver: Earned 100,000 credits (159,724)SGS LLR Silver: Earned 100,000 credits (388,159)TRP LLR Silver: Earned 100,000 credits (491,086)Woodall LLR Silver: Earned 100,000 credits (141,518)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,952,453)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,299)PPS Sieve Silver: Earned 100,000 credits (114,614)AP 26/27 Silver: Earned 100,000 credits (202,150)GFN Silver: Earned 100,000 credits (388,301)WW Silver: Earned 100,000 credits (220,000)PSA Silver: Earned 100,000 credits (292,160)
Message 149313 - Posted: 10 Mar 2021 | 18:47:12 UTC - in response to Message 149311.

Probably he did, but the next prime can be very far.
____________

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 149314 - Posted: 10 Mar 2021 | 18:56:59 UTC - in response to Message 149311.

EDIT: I'm pretty sure, if there is outside interest to run some of the K's externally with large resources and not have PG do work on them, PG admins could agree to some sort of arrangements of this kind.
Maybe I get you wrong, but this sounds like PG has to agree on such a thing. We/they don't. Anyone has the same right to work on the Riesel Problem as we do.


Correct.

We (PrimeGrid) do not own any numbers, and nobody needs our permission to use their computers as they see fit.

But that doesn't mean we have to like it.

No matter how you slice it, regardless of who talks to whom about what, this "lone-wolf" type of effort eventually will result in duplicated, wasted computer time. We don't see such a waste of computing resources as beneficial to anyone.

For now, we're going to skip further processing on these two k's, as well as any other k's for which Ryan may find a prime, but eventually *somebody* is going to go and retest all those candidates because there are some who want to know what the smallest prime is in each k. Ryan's work therefore needs to be double checked. Since we're currently using LLR2 to do fast double checking, doing full double checks on those numbers is needlessly duplicating the work he's already done. Put another way, whether Ryan does his own searching or not, we'll eventually need to test every candidate once anyway. Effectively, all of his tests amount to a waste of electricity and/or opportunity cost, since he could be using his resources to test other types of numbers that would not be duplicating effort. But it's his choice.

That being said, we are, of course, happy to have those k's eliminated.

____________
My lucky number is 75898524288+1

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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 (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,158,985)PSP LLR Silver: Earned 100,000 credits (428,457)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)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 149322 - Posted: 10 Mar 2021 | 21:36:47 UTC - in response to Message 149296.

Ryan Propper:

Let me try to clear a few things up, though I don't normally post here.

I do have a few personal machines running BOINC. I also have access to another cluster of machines, which aren't directly connected to the Internet. On these machines, I started doing some solo hunting of Riesel primes. I am explicitly searching 12e6 <= n <= 15e6. Unless I'm misunderstanding https://www.primegrid.com/stats_trp_llr.php this range should not conflict with Primegrid - now or for a while?

I don't particularly care about PrimeGrid credit, or T5K credit, or whatever. My main goal is to find primes that move the overall state of the Riesel problem forward. To that end, I undertook a solo search for some (k, n) ranges that I believed PrimeGrid was not actively investigating.

Hope that helps clear some things up.

Very nice to hear from you here!

Good to know you do 12e6 <= n <= 15e6. Is that for all of the 47 values of k?

How do you sieve before you run primality tests?

What LLR software do you use for the tests? Do you have Gerbicz check to minimize the risk of errors? You credit code LLR (not LLR2) on Top 5000.

Do you keep the sieve files? Do you keep the residues for the prime tests that come out as composite? This information could have theoretical or practical uses.

It would be nice if PrimeGrid could skip directly from n=12e6 to 15e6 when we have reached 12e6. However, that would only be clever to do so if we had precise, credible and verifiable information about how this area had already been cleared.

/JeppeSN

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 149325 - Posted: 10 Mar 2021 | 22:55:33 UTC - in response to Message 149322.

It would be nice if PrimeGrid could skip directly from n=12e6 to 15e6 when we have reached 12e6. However, that would only be clever to do so if we had precise, credible and verifiable information about how this area had already been cleared.

/JeppeSN


That won't happen. In a conjecture, a missed prime would be disastrous, and we don't trust external parties to do the computations 100% correctly. Previously, this would mean we'd double check against external residues, but with LLR2, that's pointless.
____________
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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,842,941)PPS LLR Jade: Earned 10,000,000 credits (19,232,686)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) 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 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (71,540,635)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 149331 - Posted: 11 Mar 2021 | 2:20:26 UTC

Unless external parties run LLR2 and pass us all the data we need to generate the certificate checks, right?
____________

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Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,011,570)Cullen LLR Jade: Earned 10,000,000 credits (10,009,374)ESP LLR Jade: Earned 10,000,000 credits (10,009,221)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (10,012,217)PPS LLR Jade: Earned 10,000,000 credits (16,277,057)PSP LLR Jade: Earned 10,000,000 credits (10,044,081)SoB LLR Jade: Earned 10,000,000 credits (10,064,750)SR5 LLR Jade: Earned 10,000,000 credits (10,002,051)SGS LLR Jade: Earned 10,000,000 credits (10,001,295)TRP LLR Jade: Earned 10,000,000 credits (10,002,411)Woodall LLR Jade: Earned 10,000,000 credits (10,013,921)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,004,228)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,047,667)PPS Sieve Sapphire: Earned 20,000,000 credits (20,866,490)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,043,271)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,015,177)AP 26/27 Sapphire: Earned 20,000,000 credits (20,045,194)GFN Emerald: Earned 50,000,000 credits (55,355,287)WW Sapphire: Earned 20,000,000 credits (20,160,000)PSA Double Silver: Earned 200,000,000 credits (200,301,443)
Message 149339 - Posted: 11 Mar 2021 | 7:03:59 UTC - in response to Message 149331.

Unless external parties run LLR2 and pass us all the data we need to generate the certificate checks, right?

Yes, trusted external party can generate certificate itself and pass us few lines of text output from both stages and single certificate file (1.5-2Mb per test for 12M-16M range). Such certificate can be validated by us (or anybody else) to confirm that computations were correct, eliminating need for second test.

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321 LLR Silver: Earned 100,000 credits (119,884)PPS LLR Ruby: Earned 2,000,000 credits (2,010,644)SR5 LLR Gold: Earned 500,000 credits (508,863)SGS LLR Ruby: Earned 2,000,000 credits (3,038,899)TRP LLR Gold: Earned 500,000 credits (502,390)321 Sieve (suspended) Gold: Earned 500,000 credits (512,303)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (503,510)PPS Sieve Amethyst: Earned 1,000,000 credits (1,709,097)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (34,269)TRP Sieve (suspended) Bronze: Earned 10,000 credits (32,679)AP 26/27 Silver: Earned 100,000 credits (161,720)GFN Gold: Earned 500,000 credits (500,739)PSA Silver: Earned 100,000 credits (141,661)
Message 149341 - Posted: 11 Mar 2021 | 8:08:35 UTC

As for current prime, we decided to concentrate on conjecture itself and stop testing of both this k and his previous discovery


The stats page (https://www.primegrid.com/stats_trp_llr.php) indicates that work generation is still enabled for the 2 k-values. Are they expected to be turned off soon, or are we waiting for something else before doing so?
____________
1 PPSE (+2 DC) & 5 SGS primes

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 149343 - Posted: 11 Mar 2021 | 9:35:38 UTC - in response to Message 149341.

As for current prime, we decided to concentrate on conjecture itself and stop testing of both this k and his previous discovery


The stats page (https://www.primegrid.com/stats_trp_llr.php) indicates that work generation is still enabled for the 2 k-values. Are they expected to be turned off soon, or are we waiting for something else before doing so?


They are already turned off, but there are some in the pipeline.
____________
My lucky number is 75898524288+1

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ESP LLR Bronze: Earned 10,000 credits (16,378)SR5 LLR Silver: Earned 100,000 credits (149,909)TRP LLR Silver: Earned 100,000 credits (466,404)PPS Sieve Bronze: Earned 10,000 credits (13,484)TRP Sieve (suspended) Silver: Earned 100,000 credits (496,787)
Message 150350 - Posted: 9 May 2021 | 19:59:45 UTC

why are you saying that third-party searches are a waste of resources? If the found K stop searching, then this speeds up the search for the remaining ones. it is beneficial for all of us

Michael Millerick
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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,842,941)PPS LLR Jade: Earned 10,000,000 credits (19,232,686)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) 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 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (71,540,635)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 150351 - Posted: 10 May 2021 | 2:50:10 UTC

We only know about the places where primes were found. We don’t know about all the ranges where there were no primes but have been searched. In those places, the work is being down a second and third time, which is a waste. It would be much better if the certificate files could be passed over to us to validate that the work done was correct.
____________

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 150357 - Posted: 10 May 2021 | 11:04:01 UTC - in response to Message 150350.

why are you saying that third-party searches are a waste of resources? If the found K stop searching, then this speeds up the search for the remaining ones. it is beneficial for all of us


Thank you for asking this. It is a great question.

For the sake of clarity, let's call the numbers between where PrimeGrid has searched and Propper's Prime as the "Gap Numbers".

If all we're comcerned about is finding a prime for each K in order to prove the conjecture, then you would be correct. While it is true that this is the primary concern, it's not the only concern. There is also some value in determining that all the smaller numbers (including the Gap Numbers) are composite so that an accurate accounting of the distribution of primes can be determined. For this reason, PrimeGrid has historically also made sure to fully check and double check all the numbers below each prime.

Until now, it was our intention to continue doing this, but we made the decision to not search the Gap Numbers for primes found outside of PrimeGrid.

However, since there is value in proving all those numbers are composite, I'm assuming that someone will eventually go back and test the Gap Numbers. They would need to be checked again because nobody can prove the accuracy of Propper's tests on the Gap Numbers.

Oddly enough, if LLR2 (and thus fast double checking) didn't exist, this wouldn't matter. The norm would be to run two tests on each number (a check and a double check). Propper could simply provide the residues for his tests on the Gap Numbers, and a second test could be run to confirm those residues. But with LL2, the norm is now just one test, and there's no way to confirm the Gap Number results without running two tests.

The only way to confirm the Gap Numbers is to run two tests, Propper's already completed test and a hypothetical future second test. If they had been done with LLR2's fast doublechecking, only one test would have been needed.

That's the waste of resources.

That doesn't stop us from being happy that the primes were found, moving us closer to solving the conjecture.

____________
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Found 1 prime in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,241,901)Cullen LLR Turquoise: Earned 5,000,000 credits (5,091,796)ESP LLR Turquoise: Earned 5,000,000 credits (5,231,559)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,361,077)PPS LLR Turquoise: Earned 5,000,000 credits (6,783,835)PSP LLR Turquoise: Earned 5,000,000 credits (6,179,598)SoB LLR Turquoise: Earned 5,000,000 credits (6,974,827)SR5 LLR Turquoise: Earned 5,000,000 credits (5,097,090)SGS LLR Ruby: Earned 2,000,000 credits (3,544,916)TRP LLR Turquoise: Earned 5,000,000 credits (5,088,607)Woodall LLR Ruby: Earned 2,000,000 credits (2,821,930)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,070,431)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (200,270)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,001,914)PPS Sieve Sapphire: Earned 20,000,000 credits (26,509,601)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,145,806)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,056,568)AP 26/27 Jade: Earned 10,000,000 credits (10,784,704)GFN Sapphire: Earned 20,000,000 credits (24,995,551)WW Turquoise: Earned 5,000,000 credits (9,664,000)PSA Emerald: Earned 50,000,000 credits (54,270,405)
Message 150359 - Posted: 10 May 2021 | 11:52:04 UTC - in response to Message 150357.

Maybe Primegrid should think about testing the "Gap Numbers" in another way.

First, PG should continue the search ignoring the "Gap Numbers" and focus only on numbers without prime. And for sure, there will be other primes discovered outside PG.

When all remaining TRP will be found (not if ...), and I think it will probably be in a decade (too optimistic?), PG could think about doing the Gap Numbers mainly for 2 raisons: First, computers will be far more powerful than now and second, software will also be more efficient. So doing the "Gap Numbers" at this moment should be "easy" and not too much time consuming.

This discussion can resume when TRP is finished :)
____________
Badge Score: 1*2 + 5*5 + 9*6 + 3*7 + 2*8 + 1*9 = 127

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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 (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,158,985)PSP LLR Silver: Earned 100,000 credits (428,457)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)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 150365 - Posted: 10 May 2021 | 18:04:56 UTC - in response to Message 150351.
Last modified: 10 May 2021 | 18:09:08 UTC

We only know about the places where primes were found. We don’t know about all the ranges where there were no primes but have been searched. In those places, the work is being down a second and third time, which is a waste. It would be much better if the certificate files could be passed over to us to validate that the work done was correct.

I agree with this!

We know Ryan Propper has found (chronological order, not size order):
2293*2^12918431 - 1 192971*2^14773498 - 1 206039*2^13104952 - 1
so we can skip these three k (although as Michael Goetz said, we do not know from where Propper started, so we do not know if these are minimal for their k).

But it is unlikely that Propper has found primes in every k he has searched. It would be very helpful if he would inform us where he had searched without finding anything. But whether he does or not, I think we must duplicate that work.

We do not know how many k he searches at a time. We do not know how many k he searched to a high limit without finding anything, and then abandoned.

Everybody would be even happier with his impressive finds if he provided information about what ranges he had searched, how reliable the hardware used was, whether he used Gerbicz check or otherwise verified all or a reasonable random sample of the results.

In lack of knowledge, can someone estimate how many of the rows in stats_trp_llr.php Ryan Propper has likely searched in order to find three primes of the sizes shown in the list here?

/JeppeSN

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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,842,941)PPS LLR Jade: Earned 10,000,000 credits (19,232,686)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) 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 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (71,540,635)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 150366 - Posted: 10 May 2021 | 19:28:11 UTC - in response to Message 150357.

Oddly enough, if LLR2 (and thus fast double checking) didn't exist, this wouldn't matter. The norm would be to run two tests on each number (a check and a double check). Propper could simply provide the residues for his tests on the Gap Numbers, and a second test could be run to confirm those residues. But with LL2, the norm is now just one test, and there's no way to confirm the Gap Number results without running two tests.

If he were to run and provide the output files from LLR2, wouldn't the same be achievable? Wouldn't we be able to generate just the quick verification task if we were given the correct inputs to generate it?
____________

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 150369 - Posted: 10 May 2021 | 22:03:06 UTC - in response to Message 150366.

Oddly enough, if LLR2 (and thus fast double checking) didn't exist, this wouldn't matter. The norm would be to run two tests on each number (a check and a double check). Propper could simply provide the residues for his tests on the Gap Numbers, and a second test could be run to confirm those residues. But with LL2, the norm is now just one test, and there's no way to confirm the Gap Number results without running two tests.

If he were to run and provide the output files from LLR2, wouldn't the same be achievable? Wouldn't we be able to generate just the quick verification task if we were given the correct inputs to generate it?


LLR2's does not operate in fast double check mode unless you specifically tell it to do so. Normal LLR/LLR2 command lines looks like this:

llr -d -t4 -q"12345*2^12345678+1"

Take a look at the command line on any LLR2 task. It's a lot different. It's not something you would do without explicitly trying to do so.

Furthermore, the "output files" are gigabytes upon gigabytes of proof files. I can't imagine he's running LLR2 in that mode, even less so storing those files, and these files would have to be stored somewhere until someone decided they wanted to test the Gap Numbers. It's those large proof files that let us do the fast double checks. With just the residues, a full double check is needed.
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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 150370 - Posted: 10 May 2021 | 22:07:14 UTC - in response to Message 150359.

Maybe Primegrid should think about testing the "Gap Numbers" in another way.

First, PG should continue the search ignoring the "Gap Numbers" and focus only on numbers without prime. And for sure, there will be other primes discovered outside PG.

When all remaining TRP will be found (not if ...), and I think it will probably be in a decade


I'm sure it will be done in "a" decade. But I doubt it will be the current decade, or the decade after that, or the decade after that...

I'd wager that it would be closer to a century (or centuries) than a decade, but I won't because it's unlikely I'll be around to collect. :)
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Message 150372 - Posted: 10 May 2021 | 23:06:55 UTC - in response to Message 150369.

Oddly enough, if LLR2 (and thus fast double checking) didn't exist, this wouldn't matter. The norm would be to run two tests on each number (a check and a double check). Propper could simply provide the residues for his tests on the Gap Numbers, and a second test could be run to confirm those residues. But with LL2, the norm is now just one test, and there's no way to confirm the Gap Number results without running two tests.

If he were to run and provide the output files from LLR2, wouldn't the same be achievable? Wouldn't we be able to generate just the quick verification task if we were given the correct inputs to generate it?


LLR2's does not operate in fast double check mode unless you specifically tell it to do so. Normal LLR/LLR2 command lines looks like this:

llr -d -t4 -q"12345*2^12345678+1"

Take a look at the command line on any LLR2 task. It's a lot different. It's not something you would do without explicitly trying to do so.

Furthermore, the "output files" are gigabytes upon gigabytes of proof files. I can't imagine he's running LLR2 in that mode, even less so storing those files, and these files would have to be stored somewhere until someone decided they wanted to test the Gap Numbers. It's those large proof files that let us do the fast double checks. With just the residues, a full double check is needed.

But the point is that it is possible to generate the additional files, tarball them, and ship them off to anyone that wants to quickly verify the work. Yeah, it is a couple extra steps, but it seems insanely worthwhile to do.
____________

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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 PrimesFound 1 prime in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,132,712)Cullen LLR Turquoise: Earned 5,000,000 credits (5,038,114)ESP LLR Turquoise: Earned 5,000,000 credits (6,177,890)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,277,818)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (7,956,186)SoB LLR Sapphire: Earned 20,000,000 credits (36,067,618)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,718,606)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Turquoise: Earned 5,000,000 credits (5,007,789)321 Sieve (suspended) 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 (78,031,938)WW Sapphire: Earned 20,000,000 credits (32,204,000)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 150373 - Posted: 11 May 2021 | 0:37:20 UTC - in response to Message 150372.

But the point is that it is possible to generate the additional files, tarball them, and ship them off to anyone that wants to quickly verify the work. Yeah, it is a couple extra steps, but it seems insanely worthwhile to do.


But it has to have *already* been done for the Gap Numbers. If it hasn't (and there's no reason to believe it has been, and lots of reason to believe it hasn't), then we're back to square one: if anyone is going to test those Gap Numbers, then the tests Propper has already done on them are wasted.
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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,842,941)PPS LLR Jade: Earned 10,000,000 credits (19,232,686)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) 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 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (71,540,635)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 150374 - Posted: 11 May 2021 | 5:27:19 UTC - in response to Message 150373.

But the point is that it is possible to generate the additional files, tarball them, and ship them off to anyone that wants to quickly verify the work. Yeah, it is a couple extra steps, but it seems insanely worthwhile to do.


But it has to have *already* been done for the Gap Numbers. If it hasn't (and there's no reason to believe it has been, and lots of reason to believe it hasn't), then we're back to square one: if anyone is going to test those Gap Numbers, then the tests Propper has already done on them are wasted.

Certainly what’s done is done, but that doesn’t mean that we can’t enable independent searches to do the “right” thing going forward. Perhaps having a guide that can be accessed on how to generate the needed information from LLR2 and pass the information back to PrimeGrid for people that can’t connect up to BOINC could be helpful.
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Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,011,570)Cullen LLR Jade: Earned 10,000,000 credits (10,009,374)ESP LLR Jade: Earned 10,000,000 credits (10,009,221)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (10,012,217)PPS LLR Jade: Earned 10,000,000 credits (16,277,057)PSP LLR Jade: Earned 10,000,000 credits (10,044,081)SoB LLR Jade: Earned 10,000,000 credits (10,064,750)SR5 LLR Jade: Earned 10,000,000 credits (10,002,051)SGS LLR Jade: Earned 10,000,000 credits (10,001,295)TRP LLR Jade: Earned 10,000,000 credits (10,002,411)Woodall LLR Jade: Earned 10,000,000 credits (10,013,921)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,004,228)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,047,667)PPS Sieve Sapphire: Earned 20,000,000 credits (20,866,490)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,043,271)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,015,177)AP 26/27 Sapphire: Earned 20,000,000 credits (20,045,194)GFN Emerald: Earned 50,000,000 credits (55,355,287)WW Sapphire: Earned 20,000,000 credits (20,160,000)PSA Double Silver: Earned 200,000,000 credits (200,301,443)
Message 150380 - Posted: 11 May 2021 | 15:23:19 UTC - in response to Message 150374.

Mike wrote a great explanation what happens when an "external" prime is found and what difficulties it may cause. Really, it's good when prime is found. Much worse things happens when prime is NOT found.

You may find Propper's messages above in this thread. He is searching from 12M to 15M. Now consider that he searched this range and didn't find a prime in some k's (which is expected). Will it help us? No. Single residues are untrusted. We should search this range again. Sharing residues became useless after introduction of LLR2, we're doing only one test anyway. So all these resources were completely wasted.

Certainly what’s done is done, but that doesn’t mean that we can’t enable independent searches to do the “right” thing going forward. Perhaps having a guide that can be accessed on how to generate the needed information from LLR2 and pass the information back to PrimeGrid for people that can’t connect up to BOINC could be helpful.

I'm open for communications and can explain correct LLR2 workflow to any independent searcher. But it may change searching behavior. It's not possible anymore to just load sieve file into LLR and wait until prime pops up (or not). The search must be controlled by external script on test-by-test basis (it's possible to use pregenerated batch/command file)

Since known independent searcher can be considered trusted person, LLR2 workflow can be simplified, and certificate can be created by the person itself, significantly reducing storage requirements. All what should be kept is a certificate, its length is N/8 bytes (i.e. about 1,5Mb per test) and two short text files (lresults.txt) after main text and creation of certificate. It'll be few gigabytes of data total, but it's manageable. This data should be transferred to PG where certificates and additional information will be validated, proving that test was completed correctly without any hardware of software errors.

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Message 150385 - Posted: 11 May 2021 | 20:35:40 UTC

Maybe he searched each of k = 2293, 23669, 31859, 38473, 46663, 67117, 74699, 81041, 93839, 97139, 107347, 121889, 129007, 143047, 161669, 192971, 206039, that is seventeen k values, in the interval 12M < n < 15M, and found a prime for three out of the seventeen k values?

What would be the "expected" number of k you need to search from 12M to 15M in order to find primes in three different k?

/JeppeSN

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Message 150393 - Posted: 12 May 2021 | 22:55:00 UTC - in response to Message 150385.

Nash Weight is the amount of n's remaining from 100000-110000 after being sieved to p=512.

Sum of Nash Weights (I found the Nash Weights on rieselprime.de ) of final 47 Riesel Problem k's: 7471
Sieve Weight with p=512: 0.090021 (calculated with Merten's 3rd theorem)

Integral of n from 12M to 15M of (7471/(47*10000))/(n*ln(2)*0.090021)= 0.056845
Numerator is the chance that an n will remain after being sieved to p=512, sieve weight accounts for the fact that remaining n's are more likely to be prime because they are not divisible by any small primes, n*ln(2) is from the PNT [1/lnx=1/(n*ln2) for x=2^n].

3/0.056845=53

I also used a similar method with the "n per 25000 at 1e12" value from http://www.noprimeleftbehind.net/crus/vstats_new/crus-unproven.htm and got an answer of 50.

These calculations are oversimplified, but I doubt more precision would change the answer much.

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Message 150396 - Posted: 13 May 2021 | 0:08:42 UTC - in response to Message 150393.

3/0.056845=53


If they searched every remaining k, for n from 12M to 15M, to find the three primes, it is clear that over forty k will be done twice in this range, giving an example to %-0%/.%/,%.0's question about how it could be a waste of resources.

If it had been somehow technically possible to deliver this work inside the PrimeGrid project (which may be nontrivial because the machines "aren't directly connected to the Internet"), the leading n could instead have been advanced by 3 million.

However, the calculation is not a certain indication that all k were covered.

44 k values remain, I think.

/JeppeSN


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Message 150397 - Posted: 13 May 2021 | 1:50:31 UTC - in response to Message 150393.
Last modified: 13 May 2021 | 1:51:17 UTC

Nash Weight is the amount of n's remaining from 100000-110000 after being sieved to p=512.

Out of curiosity what does p = 512 mean here? All prime numbers up to 512? Or the first 512 prime numbers? Or does it mean something else entirely?
____________
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Message 150407 - Posted: 14 May 2021 | 0:41:21 UTC - in response to Message 150397.

For my calculations, I assumed it meant all the primes up to 512. I got the definition from https://www.mersenneforum.org/showpost.php?p=172847&postcount=4.

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Message boards : The Riesel Problem : K = 192971 prime found by Propper

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