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Message boards : General discussion : New minor discoveries

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TheCruelLogician
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Joined: 24 May 18
Posts: 131
ID: 1019105
Credit: 101,528,316
RAC: 0
Found 1 prime in the 2019 Tour de Primes321 LLR Bronze: Earned 10,000 credits (15,725)Cullen LLR Bronze: Earned 10,000 credits (34,191)ESP LLR Amethyst: Earned 1,000,000 credits (1,069,462)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (651,908)PPS LLR Jade: Earned 10,000,000 credits (10,741,346)PSP LLR Bronze: Earned 10,000 credits (25,763)SoB LLR Amethyst: Earned 1,000,000 credits (1,529,599)SR5 LLR Silver: Earned 100,000 credits (278,040)SGS LLR Amethyst: Earned 1,000,000 credits (1,010,691)TRP LLR Gold: Earned 500,000 credits (565,318)Woodall LLR Bronze: Earned 10,000 credits (18,231)321 Sieve (suspended) Silver: Earned 100,000 credits (128,076)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,366,124)PPS Sieve Emerald: Earned 50,000,000 credits (57,620,503)AP 26/27 Jade: Earned 10,000,000 credits (10,196,446)WW Amethyst: Earned 1,000,000 credits (1,940,000)GFN Jade: Earned 10,000,000 credits (13,336,891)
Message 127549 - Posted: 1 Mar 2019 | 4:23:27 UTC
Last modified: 1 Mar 2019 | 4:31:01 UTC

switched to AP27 after tdp ended and found 2 AP20s in the last 4 hours. (These are the first APs I've found. Thanks to PrimeGrid Admins or nVidia developers, whoever fixed it so the GPU actually works without returning 100 errors.)
____________


Profile mikey
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Joined: 17 Mar 09
Posts: 1284
ID: 37043
Credit: 533,290,516
RAC: 15,030
Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,038,739)Cullen LLR Ruby: Earned 2,000,000 credits (2,074,615)ESP LLR Ruby: Earned 2,000,000 credits (2,243,517)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,142,353)PPS LLR Turquoise: Earned 5,000,000 credits (7,292,459)PSP LLR Ruby: Earned 2,000,000 credits (2,232,103)SoB LLR Ruby: Earned 2,000,000 credits (2,934,612)SR5 LLR Ruby: Earned 2,000,000 credits (2,053,250)SGS LLR Turquoise: Earned 5,000,000 credits (5,152,318)TRP LLR Ruby: Earned 2,000,000 credits (2,405,015)Woodall LLR Ruby: Earned 2,000,000 credits (2,014,811)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (23,770,672)Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (944,431)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,813,253)PPS Sieve Double Silver: Earned 200,000,000 credits (342,048,709)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,446,797)AP 26/27 Sapphire: Earned 20,000,000 credits (33,140,471)WW Turquoise: Earned 5,000,000 credits (7,792,000)GFN Sapphire: Earned 20,000,000 credits (49,299,387)PSA Sapphire: Earned 20,000,000 credits (20,457,430)
Message 127556 - Posted: 1 Mar 2019 | 11:13:11 UTC - in response to Message 127549.

switched to AP27 after tdp ended and found 2 AP20s in the last 4 hours. (These are the first APs I've found. Thanks to PrimeGrid Admins or nVidia developers, whoever fixed it so the GPU actually works without returning 100 errors.)


Yup there seems to be ALOT of AP20's left to find, I was crunching those for a bit and was finding several almost every day! Every once in awhile I'd go a day or so without finding one and them I'd find a stack of them again.

TheCruelLogician
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Joined: 24 May 18
Posts: 131
ID: 1019105
Credit: 101,528,316
RAC: 0
Found 1 prime in the 2019 Tour de Primes321 LLR Bronze: Earned 10,000 credits (15,725)Cullen LLR Bronze: Earned 10,000 credits (34,191)ESP LLR Amethyst: Earned 1,000,000 credits (1,069,462)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (651,908)PPS LLR Jade: Earned 10,000,000 credits (10,741,346)PSP LLR Bronze: Earned 10,000 credits (25,763)SoB LLR Amethyst: Earned 1,000,000 credits (1,529,599)SR5 LLR Silver: Earned 100,000 credits (278,040)SGS LLR Amethyst: Earned 1,000,000 credits (1,010,691)TRP LLR Gold: Earned 500,000 credits (565,318)Woodall LLR Bronze: Earned 10,000 credits (18,231)321 Sieve (suspended) Silver: Earned 100,000 credits (128,076)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,366,124)PPS Sieve Emerald: Earned 50,000,000 credits (57,620,503)AP 26/27 Jade: Earned 10,000,000 credits (10,196,446)WW Amethyst: Earned 1,000,000 credits (1,940,000)GFN Jade: Earned 10,000,000 credits (13,336,891)
Message 127562 - Posted: 1 Mar 2019 | 13:46:28 UTC - in response to Message 127556.
Last modified: 1 Mar 2019 | 13:48:50 UTC

switched to AP27 after tdp ended and found 2 AP20s in the last 4 hours. (These are the first APs I've found. Thanks to PrimeGrid Admins or nVidia developers, whoever fixed it so the GPU actually works without returning 100 errors.)


Yup there seems to be ALOT of AP20's left to find, I was crunching those for a bit and was finding several almost every day! Every once in awhile I'd go a day or so without finding one and them I'd find a stack of them again.


It seems to me that if there are infinitely many prime numbers (Euclid) and if for any n there exists arithmetic progressions of length n (Green - Tao,) it should be the case that there are infinitely many arithmetic progressions of n primes for any n. (No, I haven't taken the time to try to prove that, nor am I aware of any proof of it, but it seems to make sense.) It follows from all this that there are, then, infinitely many APs to be double checked (which is all I have managed to accomplich since my original post!)
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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1511
ID: 306875
Credit: 34,984,759
RAC: 23,002
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 (12,735,920)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 Ruby: Earned 2,000,000 credits (2,059,478)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 127565 - Posted: 1 Mar 2019 | 14:28:43 UTC - in response to Message 127562.

It seems to me that if there are infinitely many prime numbers (Euclid) and if for any n there exists arithmetic progressions of length n (Green - Tao,) it should be the case that there are infinitely many arithmetic progressions of n primes for any n. (No, I haven't taken the time to try to prove that, nor am I aware of any proof of it, but it seems to make sense.) It follows from all this that there are, then, infinitely many APs to be double checked (which is all I have managed to accomplich since my original post!)


Sure, Green–Tao means there are infinitely many AP20, and likewise infinitely many APn for any n. Of course, currently the AP27 project searches some finite "area" of numbers… /JeppeSN

TheCruelLogician
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Joined: 24 May 18
Posts: 131
ID: 1019105
Credit: 101,528,316
RAC: 0
Found 1 prime in the 2019 Tour de Primes321 LLR Bronze: Earned 10,000 credits (15,725)Cullen LLR Bronze: Earned 10,000 credits (34,191)ESP LLR Amethyst: Earned 1,000,000 credits (1,069,462)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (651,908)PPS LLR Jade: Earned 10,000,000 credits (10,741,346)PSP LLR Bronze: Earned 10,000 credits (25,763)SoB LLR Amethyst: Earned 1,000,000 credits (1,529,599)SR5 LLR Silver: Earned 100,000 credits (278,040)SGS LLR Amethyst: Earned 1,000,000 credits (1,010,691)TRP LLR Gold: Earned 500,000 credits (565,318)Woodall LLR Bronze: Earned 10,000 credits (18,231)321 Sieve (suspended) Silver: Earned 100,000 credits (128,076)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,366,124)PPS Sieve Emerald: Earned 50,000,000 credits (57,620,503)AP 26/27 Jade: Earned 10,000,000 credits (10,196,446)WW Amethyst: Earned 1,000,000 credits (1,940,000)GFN Jade: Earned 10,000,000 credits (13,336,891)
Message 128118 - Posted: 18 Mar 2019 | 21:01:52 UTC
Last modified: 18 Mar 2019 | 21:06:13 UTC

It only took 3 weeks to find an AP23...

There seemed to be a lot of interest during TDP of the frequency of finds, so I thought I'd post my results for APs (all figures rounded up to the next highest whole number; I've included approximate runtimes, but these will obviously vary by processor. The times listed are for a 1080 Ti at stock clocks).

AP 24+ no data
AP 23 1 : 1,492 ( 1 / 15.64 days)
AP 22 1 : 136 ( 1 / 1.43 days )
AP 21 1 : 50 ( 1 / 12.58 hours )
AP 20 1 : 11 ( 1 / 2.77 hours )
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Message boards : General discussion : New minor discoveries

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