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Message boards : General discussion : Catalan-Mersenne numbers

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Borek
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Joined: 27 Aug 19
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Credit: 609,767,023
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321 LLR Bronze: Earned 10,000 credits (17,000)Cullen LLR Silver: Earned 100,000 credits (127,348)ESP LLR Bronze: Earned 10,000 credits (28,007)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (40,862)PSP LLR Bronze: Earned 10,000 credits (78,397)SoB LLR Sapphire: Earned 20,000,000 credits (31,989,054)SR5 LLR Bronze: Earned 10,000 credits (11,727)TRP LLR Bronze: Earned 10,000 credits (14,566)Woodall LLR Silver: Earned 100,000 credits (132,343)PPS Sieve Double Gold: Earned 500,000,000 credits (577,192,733)AP 26/27 Silver: Earned 100,000 credits (145,548)
Message 132431 - Posted: 28 Aug 2019 | 10:38:26 UTC

Hi everybody,

I went through this forum looking for a thread talking about Catalan-Mersenne numbers, and I didn't find one.

I was wondering if the PrimeGrid project could be the place where we could calculate the C5 element of that Catalan sequence. C5 is equal to Mersenne number M170141183460469231731687303715884105728

I know this is a bit crazy because this number has about 646 millions digits...

But is it possible ? Is it mathematically relevant ?

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 (9,187,514)PSP LLR Turquoise: Earned 5,000,000 credits (5,098,748)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 (5,609,036)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 132432 - Posted: 28 Aug 2019 | 11:20:23 UTC - in response to Message 132431.

Hi everybody,

I went through this forum looking for a thread talking about Catalan-Mersenne numbers, and I didn't find one.

I was wondering if the PrimeGrid project could be the place where we could calculate the C5 element of that Catalan sequence. C5 is equal to Mersenne number M170141183460469231731687303715884105728

I know this is a bit crazy because this number has about 646 millions digits...

But is it possible ? Is it mathematically relevant ?


My understanding of the licensing of Prime95 -- and therefore of gwnum, which forms the basis of both LLR and PFGW -- prohibits anyone else from using the software on Mersenne numbers. That function is reserved to GIMPS itself.

We have no software that is not based on gwnum which can test the primality of C5, and although such software certainly exists, the best tool for the job is likely to b Prime95. I suggest, therefore, that you take your question over to the Mersenne forums, and ask there.
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Please do not PM me with support questions. Ask on the forums instead. Thank you!

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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 (9,187,514)PSP LLR Turquoise: Earned 5,000,000 credits (5,098,748)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 (5,609,036)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 132436 - Posted: 28 Aug 2019 | 11:45:32 UTC - in response to Message 132432.

I know this is a bit crazy because this number has about 646 millions digits...

But is it possible ? Is it mathematically relevant ?


Maybe I'm missing something, but I don't think C5 has 646 million digits.

According to the link you provided, C5 is 2170141183460469231731687303715884105728-1.

select format(170141183460469231731687303715884105728 * log10(2),0); +--------------------------------------------------------------+ | format(170141183460469231731687303715884105728 * log10(2),0) | +--------------------------------------------------------------+ | 51,217,599,719,369,680,000,000,000,000,000,000,000 | +--------------------------------------------------------------+


It has 51e36 digits, or 51 trillion trillion trillion digits. 646 million digits is probably possible (ignoring the licensing problem) if you had a very powerful computer and a LOT of patience, but 51 trillion trillion trillion digits is laughably beyond what we can do.
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Please do not PM me with support questions. Ask on the forums instead. Thank you!

My lucky number is 75898524288+1

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 132448 - Posted: 28 Aug 2019 | 20:56:33 UTC

Michael is right. The number has 51,217,599,719,369,681,875,006,054,625,051,616,350 digits. Or about 51 undecillion digits (short scale).

Such a number cannot be tested.

One can trial factor. But check how far it has been done already.

Remember that any factor has the form:

2 * 170141183460469231731687303715884105727 * k + 1

for some positive integer k. The k that make this factor candidate expression a prime, are 57, 62, 194, 204, 249, 348, 369, 387, 390, . . ., cf. A057440.

/JeppeSN

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Message boards : General discussion : Catalan-Mersenne numbers

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