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Message boards : AP26 - AP27 Search : AP Prime Numbers

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Michael BeckerProject donor
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Credit: 257,728,955
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Eliminated 1 conjecture "k"321 LLR Turquoise: Earned 5,000,000 credits (5,005,512)Cullen LLR Turquoise: Earned 5,000,000 credits (5,014,519)ESP LLR Turquoise: Earned 5,000,000 credits (5,076,956)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (31,539,042)PPS LLR Turquoise: Earned 5,000,000 credits (8,460,249)PSP LLR Turquoise: Earned 5,000,000 credits (5,016,050)SoB LLR Turquoise: Earned 5,000,000 credits (5,013,831)SR5 LLR Jade: Earned 10,000,000 credits (15,873,205)SGS LLR Turquoise: Earned 5,000,000 credits (5,076,722)TRP LLR Turquoise: Earned 5,000,000 credits (5,412,265)Woodall LLR Turquoise: Earned 5,000,000 credits (5,018,004)321 Sieve Turquoise: Earned 5,000,000 credits (6,303,099)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,969,265)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,094)PPS Sieve Emerald: Earned 50,000,000 credits (51,368,787)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,001,345)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,224,085)AP 26/27 Sapphire: Earned 20,000,000 credits (25,288,965)GFN Sapphire: Earned 20,000,000 credits (39,205,178)PSA Sapphire: Earned 20,000,000 credits (28,861,785)
Message 100730 - Posted: 8 Nov 2016 | 19:11:15 UTC

Hi,

i'm interested if prime numbers of AP findings are worth to be reported, and if they can displayed in the 'Top Prime Finders' table.
I'm also interested to know how long they are (how many digits in decimal), and also how big is the gap between the primes in a row (maybe i can calculate myself).

Michael

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 (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Turquoise: Earned 5,000,000 credits (5,009,577)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Turquoise: Earned 5,000,000 credits (9,114,187)PSP LLR Turquoise: Earned 5,000,000 credits (5,065,592)SoB LLR Sapphire: Earned 20,000,000 credits (34,221,148)SR5 LLR Turquoise: Earned 5,000,000 credits (8,293,415)SGS LLR Ruby: Earned 2,000,000 credits (2,014,138)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 (5,555,366)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 Jade: Earned 10,000,000 credits (10,114,260)GFN Emerald: Earned 50,000,000 credits (66,792,810)PSA Jade: Earned 10,000,000 credits (12,404,447)
Message 100734 - Posted: 8 Nov 2016 | 21:00:18 UTC - in response to Message 100730.

Hi,

i'm interested if prime numbers of AP findings are worth to be reported, and if they can displayed in the 'Top Prime Finders' table.
I'm also interested to know how long they are (how many digits in decimal), and also how big is the gap between the primes in a row (maybe i can calculate myself).

Michael


The prime numbers themselves are not particularly interesting. They're very small. It's the fact that they form a long sequence of prime numbers that makes them interesting.

For example, the first prime number in the AP26 discovered recently is 149836681069944461. That's 18 digits. That's about 388 thousand digits too small to qualify for the Top 5000 primes.
____________
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Michael BeckerProject donor
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Joined: 3 Apr 11
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ID: 93509
Credit: 257,728,955
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Eliminated 1 conjecture "k"321 LLR Turquoise: Earned 5,000,000 credits (5,005,512)Cullen LLR Turquoise: Earned 5,000,000 credits (5,014,519)ESP LLR Turquoise: Earned 5,000,000 credits (5,076,956)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (31,539,042)PPS LLR Turquoise: Earned 5,000,000 credits (8,460,249)PSP LLR Turquoise: Earned 5,000,000 credits (5,016,050)SoB LLR Turquoise: Earned 5,000,000 credits (5,013,831)SR5 LLR Jade: Earned 10,000,000 credits (15,873,205)SGS LLR Turquoise: Earned 5,000,000 credits (5,076,722)TRP LLR Turquoise: Earned 5,000,000 credits (5,412,265)Woodall LLR Turquoise: Earned 5,000,000 credits (5,018,004)321 Sieve Turquoise: Earned 5,000,000 credits (6,303,099)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,969,265)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,094)PPS Sieve Emerald: Earned 50,000,000 credits (51,368,787)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,001,345)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,224,085)AP 26/27 Sapphire: Earned 20,000,000 credits (25,288,965)GFN Sapphire: Earned 20,000,000 credits (39,205,178)PSA Sapphire: Earned 20,000,000 credits (28,861,785)
Message 100739 - Posted: 8 Nov 2016 | 21:33:58 UTC - in response to Message 100734.

Hi Michael,

thank you for the information.
I didn't thought that they are so small.

Michael

Yair GivoniProject donor
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Discovered 1 mega prime321 LLR Silver: Earned 100,000 credits (104,357)Cullen LLR Bronze: Earned 10,000 credits (83,851)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (13,147)PPS LLR Ruby: Earned 2,000,000 credits (3,403,064)PSP LLR Gold: Earned 500,000 credits (536,893)SoB LLR Sapphire: Earned 20,000,000 credits (20,330,503)SR5 LLR Bronze: Earned 10,000 credits (21,624)SGS LLR Amethyst: Earned 1,000,000 credits (1,596,638)TRP LLR Amethyst: Earned 1,000,000 credits (1,202,505)Woodall LLR Silver: Earned 100,000 credits (362,081)Generalized Cullen/Woodall Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,247,364)PPS Sieve Turquoise: Earned 5,000,000 credits (6,469,018)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,421,388)TRP Sieve (suspended) Silver: Earned 100,000 credits (150,475)AP 26/27 Emerald: Earned 50,000,000 credits (74,508,801)GFN Double Bronze: Earned 100,000,000 credits (136,585,260)
Message 109263 - Posted: 8 Aug 2017 | 6:49:52 UTC
Last modified: 8 Aug 2017 | 6:50:53 UTC

Curiosity, does anybody know what happens primenumberwise in between the primes in the AP series? Does AP series overlap?

Profile JeppeSNProject donor
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321 LLR Silver: Earned 100,000 credits (360,928)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 Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109315 - Posted: 11 Aug 2017 | 13:03:15 UTC - in response to Message 109263.

Curiosity, does anybody know what happens primenumberwise in between the primes in the AP series? Does AP series overlap?


There will almost always be other primes in between the primes in an AP series.

Finding an instance where that is not the case, is much harder; it is called a CPAP with the terminology used e.g. in http://primerecords.dk/.

For your other question, yes, AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.

/JeppeSN

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Discovered 2 mega primesFound 1 prime in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,477,467)Cullen LLR Gold: Earned 500,000 credits (776,297)ESP LLR Ruby: Earned 2,000,000 credits (3,120,351)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,056,207)PPS LLR Jade: Earned 10,000,000 credits (12,244,808)PSP LLR Turquoise: Earned 5,000,000 credits (5,000,271)SoB LLR Sapphire: Earned 20,000,000 credits (20,302,727)SR5 LLR Turquoise: Earned 5,000,000 credits (5,978,312)SGS LLR Ruby: Earned 2,000,000 credits (2,940,587)TRP LLR Turquoise: Earned 5,000,000 credits (7,025,303)Woodall LLR Amethyst: Earned 1,000,000 credits (1,693,614)321 Sieve Jade: Earned 10,000,000 credits (19,959,403)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,571,178)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,009,610)PPS Sieve Double Silver: Earned 200,000,000 credits (243,562,113)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,165,888)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,071,454)AP 26/27 Turquoise: Earned 5,000,000 credits (6,300,774)GFN Emerald: Earned 50,000,000 credits (50,062,736)PSA Double Bronze: Earned 100,000,000 credits (102,762,384)
Message 109316 - Posted: 11 Aug 2017 | 13:31:35 UTC - in response to Message 109315.

AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.

Also, AP series may have primes in common. For example {31, 37, 43} and {19, 31, 43}.

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321 LLR Silver: Earned 100,000 credits (360,928)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 Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109319 - Posted: 11 Aug 2017 | 17:28:00 UTC - in response to Message 109316.

AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.

Also, AP series may have primes in common. For example {31, 37, 43} and {19, 31, 43}.


And you expect each odd prime p to be a member of infinitely many arithmetic progressions of primes.

However, for a fixed prime p, the length of the APs it can be a member of is bounded. For example, for p=31, no AP of primes (one of which is 31) can have a length of 32 (or more), because then one other member of the AP would be a multiple of 31, and hence composite.

/JeppeSN

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321 LLR Silver: Earned 100,000 credits (104,482)Cullen LLR Silver: Earned 100,000 credits (102,670)ESP LLR Silver: Earned 100,000 credits (104,502)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (114,572)PPS LLR Silver: Earned 100,000 credits (102,015)PSP LLR Silver: Earned 100,000 credits (118,657)SoB LLR Sapphire: Earned 20,000,000 credits (24,448,529)SR5 LLR Silver: Earned 100,000 credits (100,043)SGS LLR Silver: Earned 100,000 credits (105,539)TRP LLR Silver: Earned 100,000 credits (106,264)Woodall LLR Silver: Earned 100,000 credits (107,466)321 Sieve Silver: Earned 100,000 credits (140,910)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,005,637)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (104,861)PPS Sieve Ruby: Earned 2,000,000 credits (4,033,489)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (15,365,882)TRP Sieve (suspended) Silver: Earned 100,000 credits (119,061)AP 26/27 Silver: Earned 100,000 credits (105,118)GFN Silver: Earned 100,000 credits (250,199)PSA Silver: Earned 100,000 credits (131,126)
Message 109320 - Posted: 11 Aug 2017 | 18:09:13 UTC

Are AP series generally interesting mathematical oddities only, or is there an application where they can be put to use in the real world?

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321 LLR Silver: Earned 100,000 credits (360,928)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 Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109325 - Posted: 12 Aug 2017 | 12:01:48 UTC - in response to Message 109320.

Are AP series generally interesting mathematical oddities only, or is there an application where they can be put to use in the real world?


Mathematics is the real world, you know. Everything else is just impure approximations to it.

But I do not think there are any practical applications. The main result (2004) is that they come in all lengths (Green–Tao, free access to full article The primes contain arbitrarily long arithmetic progressions (2008)).

/JeppeSN

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Joined: 27 Feb 10
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Credit: 49,771,023
RAC: 3,127
321 LLR Silver: Earned 100,000 credits (104,482)Cullen LLR Silver: Earned 100,000 credits (102,670)ESP LLR Silver: Earned 100,000 credits (104,502)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (114,572)PPS LLR Silver: Earned 100,000 credits (102,015)PSP LLR Silver: Earned 100,000 credits (118,657)SoB LLR Sapphire: Earned 20,000,000 credits (24,448,529)SR5 LLR Silver: Earned 100,000 credits (100,043)SGS LLR Silver: Earned 100,000 credits (105,539)TRP LLR Silver: Earned 100,000 credits (106,264)Woodall LLR Silver: Earned 100,000 credits (107,466)321 Sieve Silver: Earned 100,000 credits (140,910)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,005,637)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (104,861)PPS Sieve Ruby: Earned 2,000,000 credits (4,033,489)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (15,365,882)TRP Sieve (suspended) Silver: Earned 100,000 credits (119,061)AP 26/27 Silver: Earned 100,000 credits (105,118)GFN Silver: Earned 100,000 credits (250,199)PSA Silver: Earned 100,000 credits (131,126)
Message 109332 - Posted: 12 Aug 2017 | 19:07:06 UTC - in response to Message 109325.

Mathematics is the real world, you know. Everything else is just impure approximations to it.


Never heard it that way before, but I like it.

But I do not think there are any practical applications.


Thanks, for some reason, in my head, I seem to get them crossed with the optimal Golomb rulers that distributed.net is working on.

Message boards : AP26 - AP27 Search : AP Prime Numbers

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