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Message boards : Proth Prime Search : Fermat divisors by year

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Profile JeppeSNProject donor
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321 LLR Silver: Earned 100,000 credits (268,229)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 Amethyst: Earned 1,000,000 credits (1,893,206)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 124298 - Posted: 4 Jan 2019 | 16:27:39 UTC

If you search PrimeGrid primes for Fermat divisors, you get this list (For the oldest two, I found the year on the Top 5000 site):

2018: 0 found

2017: 0 found

2016: 0 found

2015: 1 found (267*2^2662090+1)

2014: 1 found (193*2^3329782+1)

2013: 3 found (2145*2^1099064+1; 57*2^2747499+1; 183*2^1747660+1)

2012: 4 found (1705*2^906110+1; 7905*2^352281+1; 131*2^1494099+1; 329*2^1246017+1)

2011: 5 found (25*2^2141884+1; 4479*2^226618+1; 3771*2^221676+1; 9*2^2543551+1; 7333*2^138560+1)

2010: 0 found

2009: 2 found (659*2^617815+1; 519*2^567235+1)

2008: 1 found (651*2^476632+1)

2007: 1 found (151*2^585044+1)

2006: 0 found

2005: 1 found (27*2^672007+1)

This makes me wonder:

When will PrimeGrid find its next Fermat divisor (apparently its twentieth)?

Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?

/JeppeSN

Profile Michael GoetzProject donor
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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 Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (3,820,430)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Ruby: Earned 2,000,000 credits (2,773,744)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (34,158,496)SR5 LLR Turquoise: Earned 5,000,000 credits (8,293,415)SGS LLR Ruby: Earned 2,000,000 credits (2,012,781)TRP LLR Ruby: Earned 2,000,000 credits (2,737,347)Woodall LLR Ruby: Earned 2,000,000 credits (2,195,123)321 Sieve Turquoise: Earned 5,000,000 credits (5,046,112)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 (20,110,788)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 Turquoise: Earned 5,000,000 credits (7,118,397)GFN Emerald: Earned 50,000,000 credits (64,595,124)PSA Jade: Earned 10,000,000 credits (10,135,447)
Message 124300 - Posted: 4 Jan 2019 | 16:32:16 UTC - in response to Message 124298.

Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?

/JeppeSN


The numbers we're testing are a lot bigger and primes are harder to find?
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Scott BrownProject donor
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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 13 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 1 Fermat divisor2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes321 LLR Double Bronze: Earned 100,000,000 credits (100,829,118)Cullen LLR Double Bronze: Earned 100,000,000 credits (103,870,990)ESP LLR Double Bronze: Earned 100,000,000 credits (114,443,502)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (108,461,080)PPS LLR Double Silver: Earned 200,000,000 credits (343,575,390)PSP LLR Double Bronze: Earned 100,000,000 credits (108,003,110)SoB LLR Double Bronze: Earned 100,000,000 credits (135,747,083)SR5 LLR Double Silver: Earned 200,000,000 credits (201,210,377)SGS LLR Double Bronze: Earned 100,000,000 credits (160,908,586)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Bronze: Earned 100,000,000 credits (121,443,822)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,447,725)321 Sieve Double Silver: Earned 200,000,000 credits (203,510,966)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,107,819,760)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Bronze: Earned 100,000,000 credits (119,562,131)GFN Double Amethyst: Earned 1,000,000,000 credits (1,222,501,936)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 124301 - Posted: 4 Jan 2019 | 16:59:54 UTC - in response to Message 124300.

Is there a good explanation (mathematical and/or technical) why we have seen relatively few Fermat divisors recently, or is that simply a conincidence?

/JeppeSN


The numbers we're testing are a lot bigger and primes are harder to find?


I would add also the following:

1) in the earlier years, PPSE was largely the only game in town. We have a vastly broader set of sub-projects now than in prior years, and this means that a smaller proportion of our efforts are placed in the proth prime projects where we usually find Fermat divisors.

2) Proth primes have been further divided into PPSE, PPS, and PPS-mega. Thus, our efforts likely to find divisors are even further diminished as considerable PPS effort is focused on finding a mega prime, which is less likely to yield primes overall than PPSE, and thus, divisors.

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Message boards : Proth Prime Search : Fermat divisors by year

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