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Message boards : Number crunching : Which conjecture most likely to find a prime?

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zombie67 [MM]Project donor
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Discovered 14 mega primesEliminated 1 conjecture "k"Found 3 primes in the 2020 Tour de PrimesFound 1 mega prime in the 2020 Tour de PrimesFound 3 primes in the 2021 Tour de PrimesFound 3 mega primes in the 2021 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (20,140,357)Cullen LLR Sapphire: Earned 20,000,000 credits (20,612,581)ESP LLR Sapphire: Earned 20,000,000 credits (22,418,766)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (16,908,506)PPS LLR Emerald: Earned 50,000,000 credits (81,868,361)PSP LLR Jade: Earned 10,000,000 credits (16,559,093)SoB LLR Sapphire: Earned 20,000,000 credits (21,425,737)SR5 LLR Sapphire: Earned 20,000,000 credits (26,176,906)SGS LLR Jade: Earned 10,000,000 credits (13,827,516)TRP LLR Sapphire: Earned 20,000,000 credits (22,255,184)Woodall LLR Sapphire: Earned 20,000,000 credits (20,056,234)321 Sieve (suspended) Emerald: Earned 50,000,000 credits (50,559,131)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,297,856)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,711,622)PPS Sieve Double Gold: Earned 500,000,000 credits (652,202,364)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (11,707,274)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,316,578)AP 26/27 Double Silver: Earned 200,000,000 credits (201,132,769)WW Double Silver: Earned 200,000,000 credits (415,156,000)GFN Double Silver: Earned 200,000,000 credits (428,195,553)PSA Emerald: Earned 50,000,000 credits (52,054,411)
Message 144244 - Posted: 17 Oct 2020 | 1:57:00 UTC
Last modified: 17 Oct 2020 | 2:01:53 UTC

If I understand correctly, there are five conjecture sub-projects: ESP, PSP, TRP, SOB, and SR5. Which of these is the most likely (easiest?) to find a prime?

I am hunting K badges. =;^)
____________
Reno, NV

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Discovered the World's First base 25 Generalized Cullen prime!!!Discovered 37 mega primesEliminated 2 conjecture "k"sDiscovered 2 AP26sDiscovered 1 twin primeDiscovered 1 Fermat divisor2017 Tour de Primes highest prime count2017 Tour de Primes most Mountain Stage primes2018 Tour de Primes most Mountain Stage primesFound 4 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 4 primes in the 2018 Tour de Primes Mountain StageFound 1 mega prime in the 2018 Tour de Primes Mountain StageFound 1 prime in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de Primes2020 Tour de Primes largest primeFound 3 primes in the 2020 Tour de PrimesFound 2 mega primes in the 2020 Tour de Primes2021 Tour de Primes most Mountain Stage primesFound 9 primes in the 2021 Tour de PrimesFound 6 mega primes in the 2021 Tour de PrimesFound 3 primes in the 2021 Tour de Primes Mountain StageFound 1 mega prime  in the 2021 Tour de Primes Mountain Stage321 LLR Double Bronze: Earned 100,000,000 credits (151,225,513)Cullen LLR Double Silver: Earned 200,000,000 credits (200,281,447)ESP LLR Double Bronze: Earned 100,000,000 credits (197,414,734)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (151,664,290)PPS LLR Double Gold: Earned 500,000,000 credits (679,138,368)PSP LLR Double Bronze: Earned 100,000,000 credits (157,167,806)SoB LLR Double Silver: Earned 200,000,000 credits (407,591,534)SR5 LLR Double Bronze: Earned 100,000,000 credits (151,448,183)SGS LLR Double Bronze: Earned 100,000,000 credits (154,607,703)TRP LLR Double Silver: Earned 200,000,000 credits (288,859,432)Woodall LLR Double Silver: Earned 200,000,000 credits (200,946,877)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (134,986,204)Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (30,879,764)Generalized Cullen/Woodall Sieve (suspended) Double Bronze: Earned 100,000,000 credits (100,428,955)PPS Sieve Double Turquoise: Earned 5,000,000,000 credits (5,158,365,499)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Bronze: Earned 100,000,000 credits (101,857,516)TRP Sieve (suspended) Emerald: Earned 50,000,000 credits (50,936,081)AP 26/27 Double Ruby: Earned 2,000,000,000 credits (2,194,119,928)WW Double Turquoise: Earned 5,000,000,000 credits (6,164,068,000)GFN Double Turquoise: Earned 5,000,000,000 credits (6,500,197,606)PSA Double Turquoise: Earned 5,000,000,000 credits (6,051,240,385)
Message 144246 - Posted: 17 Oct 2020 | 2:06:27 UTC - in response to Message 144244.

If I understand correctly, there are five conjecture sub-projects: ESP, PSP, TRP, SOB, and SR5. Which of these is the most likely (easiest?) to find a prime?

I am hunting K badges. =;^)


SR5 is searching for the smallest primes, and I'm pretty sure that's what matters.

Good luck bagging one!
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321 LLR Silver: Earned 100,000 credits (195,722)Cullen LLR Silver: Earned 100,000 credits (112,212)ESP LLR Silver: Earned 100,000 credits (219,395)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (206,330)PPS LLR Amethyst: Earned 1,000,000 credits (1,982,797)PSP LLR Silver: Earned 100,000 credits (100,559)SoB LLR Gold: Earned 500,000 credits (533,625)SR5 LLR Silver: Earned 100,000 credits (103,183)SGS LLR Silver: Earned 100,000 credits (107,487)TRP LLR Silver: Earned 100,000 credits (109,075)Woodall LLR Silver: Earned 100,000 credits (117,864)321 Sieve (suspended) Gold: Earned 500,000 credits (506,814)Generalized Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (30,033)PPS Sieve Ruby: Earned 2,000,000 credits (2,808,043)AP 26/27 Gold: Earned 500,000 credits (800,514)WW Amethyst: Earned 1,000,000 credits (1,336,000)GFN Ruby: Earned 2,000,000 credits (2,199,944)PSA Silver: Earned 100,000 credits (373,034)
Message 144249 - Posted: 17 Oct 2020 | 3:35:41 UTC
Last modified: 17 Oct 2020 | 3:35:50 UTC

TRP has been an abnormally long time without a prime k.
____________
SHSIDElectronicsGroup@outlook.com

waiting for a TdP prime...
Proth "SoB": 44243*2^440969+1


Profile JeppeSNProject donor
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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 Jade: Earned 10,000,000 credits (12,265,537)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 144256 - Posted: 17 Oct 2020 | 8:41:24 UTC - in response to Message 144246.

If I understand correctly, there are five conjecture sub-projects: ESP, PSP, TRP, SOB, and SR5. Which of these is the most likely (easiest?) to find a prime?

I am hunting K badges. =;^)


SR5 is searching for the smallest primes, and I'm pretty sure that's what matters.

Good luck bagging one!


Agree. From the front page today:
23 CPU Extended Sierpinski Problem (LLR) 13 CPU Prime Sierpinski Problem (LLR) 8 CPU Seventeen or Bust (LLR) 73 CPU Sierpinski / Riesel Base 5 Problem (LLR) 46 CPU The Riesel Problem (LLR)


So SR5 ranks lowest at 73rd position on the Top 100 list, so highest density of primes there. Are base 5 candidates less efficient to test than base 2, with LLR2?

/JeppeSN

Pavel Atnashev
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Discovered 3 mega primesEliminated 2 conjecture "k"s321 LLR Jade: Earned 10,000,000 credits (11,980,856)Cullen LLR Emerald: Earned 50,000,000 credits (71,772,873)ESP LLR Double Gold: Earned 500,000,000 credits (974,840,254)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,073)PPS LLR Double Bronze: Earned 100,000,000 credits (133,968,831)PSP LLR Double Silver: Earned 200,000,000 credits (273,829,354)SoB LLR Double Amethyst: Earned 1,000,000,000 credits (1,010,504,273)SR5 LLR Double Bronze: Earned 100,000,000 credits (100,345,041)TRP LLR Double Silver: Earned 200,000,000 credits (257,876,275)Woodall LLR Ruby: Earned 2,000,000 credits (4,756,356)Generalized Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (24,029)
Message 144262 - Posted: 17 Oct 2020 | 11:07:24 UTC - in response to Message 144256.

Yes, but with a linear coefficient.

zombie67 [MM]Project donor
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Discovered 14 mega primesEliminated 1 conjecture "k"Found 3 primes in the 2020 Tour de PrimesFound 1 mega prime in the 2020 Tour de PrimesFound 3 primes in the 2021 Tour de PrimesFound 3 mega primes in the 2021 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (20,140,357)Cullen LLR Sapphire: Earned 20,000,000 credits (20,612,581)ESP LLR Sapphire: Earned 20,000,000 credits (22,418,766)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (16,908,506)PPS LLR Emerald: Earned 50,000,000 credits (81,868,361)PSP LLR Jade: Earned 10,000,000 credits (16,559,093)SoB LLR Sapphire: Earned 20,000,000 credits (21,425,737)SR5 LLR Sapphire: Earned 20,000,000 credits (26,176,906)SGS LLR Jade: Earned 10,000,000 credits (13,827,516)TRP LLR Sapphire: Earned 20,000,000 credits (22,255,184)Woodall LLR Sapphire: Earned 20,000,000 credits (20,056,234)321 Sieve (suspended) Emerald: Earned 50,000,000 credits (50,559,131)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,297,856)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,711,622)PPS Sieve Double Gold: Earned 500,000,000 credits (652,202,364)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (11,707,274)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,316,578)AP 26/27 Double Silver: Earned 200,000,000 credits (201,132,769)WW Double Silver: Earned 200,000,000 credits (415,156,000)GFN Double Silver: Earned 200,000,000 credits (428,195,553)PSA Emerald: Earned 50,000,000 credits (52,054,411)
Message 144323 - Posted: 18 Oct 2020 | 13:35:08 UTC

Thanks guys. I will run SR5.

I did not know that smallest = easiest to find. Out of curiosity, why is that? I understand that smallest probably means the tasks run fastest, so you can run more tasks in a given amount of time. But couldn't it also be true that there may just be less primes to find in a particular conjecture, and therefore less likely to find primes? I guess I don't understand the relationship between the size of the prime and the likelihood of finding one.
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Reno, NV

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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 Ruby: Earned 2,000,000 credits (4,934,619)ESP LLR Turquoise: Earned 5,000,000 credits (5,766,255)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Sapphire: Earned 20,000,000 credits (20,751,038)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)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 Ruby: Earned 2,000,000 credits (2,963,361)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)WW Sapphire: Earned 20,000,000 credits (31,412,000)GFN Emerald: Earned 50,000,000 credits (77,916,132)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 144326 - Posted: 18 Oct 2020 | 14:14:57 UTC - in response to Message 144323.

Thanks guys. I will run SR5.

I did not know that smallest = easiest to find. Out of curiosity, why is that? I understand that smallest probably means the tasks run fastest, so you can run more tasks in a given amount of time. But couldn't it also be true that there may just be less primes to find in a particular conjecture, and therefore less likely to find primes? I guess I don't understand the relationship between the size of the prime and the likelihood of finding one.


Primes become rarer as the numbers get larger. And, as you noted, the tests get longer.

When you combine both factors, the "difficulty" of finding a prime is proportional to slightly more than the cube of the size of the number. Another way to look at is if you double the size of the number, it will take you about 10 times longer to find a prime.

There's other factors, of course. Some types of primes use faster testing methods, more sieving lowers the time needed to find a prime, etc. But other things being equal. just doubling the size of the number increases the difficulty (time) of finding a prime by roughly tenfold.
____________
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Discovered 14 mega primesEliminated 1 conjecture "k"Found 3 primes in the 2020 Tour de PrimesFound 1 mega prime in the 2020 Tour de PrimesFound 3 primes in the 2021 Tour de PrimesFound 3 mega primes in the 2021 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (20,140,357)Cullen LLR Sapphire: Earned 20,000,000 credits (20,612,581)ESP LLR Sapphire: Earned 20,000,000 credits (22,418,766)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (16,908,506)PPS LLR Emerald: Earned 50,000,000 credits (81,868,361)PSP LLR Jade: Earned 10,000,000 credits (16,559,093)SoB LLR Sapphire: Earned 20,000,000 credits (21,425,737)SR5 LLR Sapphire: Earned 20,000,000 credits (26,176,906)SGS LLR Jade: Earned 10,000,000 credits (13,827,516)TRP LLR Sapphire: Earned 20,000,000 credits (22,255,184)Woodall LLR Sapphire: Earned 20,000,000 credits (20,056,234)321 Sieve (suspended) Emerald: Earned 50,000,000 credits (50,559,131)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,297,856)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,711,622)PPS Sieve Double Gold: Earned 500,000,000 credits (652,202,364)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (11,707,274)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,316,578)AP 26/27 Double Silver: Earned 200,000,000 credits (201,132,769)WW Double Silver: Earned 200,000,000 credits (415,156,000)GFN Double Silver: Earned 200,000,000 credits (428,195,553)PSA Emerald: Earned 50,000,000 credits (52,054,411)
Message 144333 - Posted: 18 Oct 2020 | 15:39:04 UTC

Thanks for the explanation.
____________
Reno, NV

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Message boards : Number crunching : Which conjecture most likely to find a prime?

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