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Message boards : AP26 - AP27 Search : What algorithm is used to find AP?

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Endead383
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Credit: 1,646,409
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321 LLR Bronze: Earned 10,000 credits (29,191)PPS LLR Bronze: Earned 10,000 credits (53,942)SGS LLR Bronze: Earned 10,000 credits (81,264)321 Sieve (suspended) Bronze: Earned 10,000 credits (15,247)PPS Sieve Silver: Earned 100,000 credits (232,599)AP 26/27 Gold: Earned 500,000 credits (525,590)GFN Gold: Earned 500,000 credits (691,855)
Message 129746 - Posted: 23 May 2019 | 18:41:34 UTC

My question is: what algorithm is used to find APs?

I'm going to use my big AP but i think is the same at all the others

185164481362593913+121857779*23#*n for n=0..20

I found that 185164481362593913 is prime and 121857779 too, I would like know how the sistem select them.


END383

____________
123547534^32768+1 (GFN 15) 265154 digits

34945494^16384+1 (GFN 14) 123591 digits

157959668^8192+1 (GFN 13) 67,163 digits

Ravi Fernando
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321 LLR Silver: Earned 100,000 credits (481,812)Cullen LLR Bronze: Earned 10,000 credits (82,217)ESP LLR Bronze: Earned 10,000 credits (16,570)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (12,551)PPS LLR Ruby: Earned 2,000,000 credits (2,565,397)PSP LLR Bronze: Earned 10,000 credits (26,371)SoB LLR Silver: Earned 100,000 credits (258,849)SR5 LLR Bronze: Earned 10,000 credits (59,307)SGS LLR Silver: Earned 100,000 credits (148,878)TRP LLR Silver: Earned 100,000 credits (195,905)Woodall LLR Bronze: Earned 10,000 credits (19,925)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,001,667)AP 26/27 Bronze: Earned 10,000 credits (72,774)WW Bronze: Earned 10,000 credits (12,000)GFN Silver: Earned 100,000 credits (248,769)
Message 129748 - Posted: 23 May 2019 | 19:17:17 UTC - in response to Message 129746.
Last modified: 23 May 2019 | 19:17:37 UTC

This thread has some general information about the AP search. The algorithm was designed by Jarosław Wróblewski, who gives a summary of it here:
How to search for 26 primes in arithmetic progression?.

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 (11,800,086)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 (9,268,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 129768 - Posted: 24 May 2019 | 14:58:36 UTC

It is true that 121857779 is a prime, but that is insignificant.

You have found another AP:

140980475961780677+121745694*23#*n for n=0..20

and 121745694 is not a prime. (It is 2 * 3 * 7^2 * 414101.)

Not sure if this is what you ask, but from the list of your AP finds, if you click on each line, you can see the primes that constitute the progression.

For an AP21, there are 21 primes in the progression, and they are positioned with uniform spacing on a number line.

/JeppeSN

Message boards : AP26 - AP27 Search : What algorithm is used to find AP?

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