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Message boards : General discussion : Numbers like GFN

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Profile Crun-chiProject donor
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Joined: 25 Nov 09
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Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 68953 - Posted: 5 Sep 2013 | 23:09:46 UTC
Last modified: 5 Sep 2013 | 23:11:52 UTC

As I can see, those numbers have N= 65536, 131072, 262144....

Three questions:

1. Can I made sieve and search primes for example N=111111 (k*111111+1)
2. How to make that sieve?
3. Is it will be any primes in such condition :) ?

I know in that case it wont be GF numbers, but will be something that never be searched :)
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Iain BethuneProject donor
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Credit: 194,056,043
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321 LLR Gold: Earned 500,000 credits (597,175)Cullen LLR Amethyst: Earned 1,000,000 credits (1,355,381)ESP LLR Turquoise: Earned 5,000,000 credits (5,048,594)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,564,412)PPS LLR Amethyst: Earned 1,000,000 credits (1,025,115)PSP LLR Sapphire: Earned 20,000,000 credits (28,367,849)SoB LLR Jade: Earned 10,000,000 credits (16,215,329)SR5 LLR Turquoise: Earned 5,000,000 credits (5,189,992)SGS LLR Amethyst: Earned 1,000,000 credits (1,244,067)TRP LLR Turquoise: Earned 5,000,000 credits (5,169,405)Woodall LLR Amethyst: Earned 1,000,000 credits (1,070,956)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,003)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (200,371)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (11,645,025)PPS Sieve Turquoise: Earned 5,000,000 credits (7,536,532)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,017,144)TRP Sieve (suspended) Gold: Earned 500,000 credits (554,946)AP 26/27 Ruby: Earned 2,000,000 credits (3,577,848)GFN Emerald: Earned 50,000,000 credits (97,047,976)PSA Ruby: Earned 2,000,000 credits (4,606,694)
Message 68959 - Posted: 6 Sep 2013 | 9:57:19 UTC - in response to Message 68953.

Hi Crun-chi,

No idea on the sieving (although one could do a simple trial division filter). But in general, testing such numbers for primes will be really slow, so you will be stuck with small numbers i.e. below top5000 list. Fast tests only exist for a range of particular forms e.g. Proth, Riesel, Mersenne, GFN, Primorial etc.

Probably best thing to look at is: http://mersennewiki.org/index.php/Primality_test or check out LLR and PFGW as they implement almost all of the fast deterministics tests and PRP checks.

Otherwise you'll be using ECPP - for reference the record ECPP-proved prime has a little over 26,000 digits! http://primes.utm.edu/top20/page.php?id=27

As always, happy hunting!

- Iain
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3073428256125*2^1290000-1 is Prime!

Profile Crun-chiProject donor
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Joined: 25 Nov 09
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Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 68961 - Posted: 6 Sep 2013 | 11:31:49 UTC - in response to Message 68959.

Thanks for answer my question :)
Since only speed can provide to me number of candidates& better probability I am forced to stick with "ordinary" sieving and prime proving methods, and my idea dont stick with no one above :)

____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Ken_g6Project donor
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Credit: 220,694,886
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Discovered 1 mega primeFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,010,094)Cullen LLR Ruby: Earned 2,000,000 credits (2,022,806)ESP LLR Amethyst: Earned 1,000,000 credits (1,657,625)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (767,102)PPS LLR Sapphire: Earned 20,000,000 credits (24,726,694)PSP LLR Turquoise: Earned 5,000,000 credits (5,182,638)SoB LLR Turquoise: Earned 5,000,000 credits (5,923,035)SR5 LLR Ruby: Earned 2,000,000 credits (2,061,736)SGS LLR Ruby: Earned 2,000,000 credits (2,139,194)TPS LLR (retired) Bronze: Earned 10,000 credits (19,376)TRP LLR Ruby: Earned 2,000,000 credits (2,520,745)Woodall LLR Ruby: Earned 2,000,000 credits (2,021,413)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,915,071)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,584,236)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,461,309)PPS Sieve Emerald: Earned 50,000,000 credits (92,950,614)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (352,129)TRP Sieve (suspended) Gold: Earned 500,000 credits (776,202)AP 26/27 Turquoise: Earned 5,000,000 credits (5,851,049)GFN Sapphire: Earned 20,000,000 credits (35,632,932)WW Jade: Earned 10,000,000 credits (15,964,000)PSA Ruby: Earned 2,000,000 credits (4,154,617)
Message 69051 - Posted: 10 Sep 2013 | 0:09:31 UTC

If you meant to say k^111111+1, looks like the answer is no. In your case, apparently, k^37037+1 | k^111111+1 (for all k!)

It apparently doesn't work for -1 either.
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Profile Crun-chiProject donor
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Joined: 25 Nov 09
Posts: 3069
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RAC: 486
Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 69089 - Posted: 11 Sep 2013 | 12:18:26 UTC - in response to Message 69051.

So my idea is useless :)
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie!

Message boards : General discussion : Numbers like GFN

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