mersenneforum.org Mersenne number with exponent 333333367 is composite
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 2019-05-05, 11:38 #1 TheGuardian   May 2019 68 Posts Mersenne number with exponent 333333367 is composite Hi all, I'm not sure where to post this as I'm new to these forums but I recently completed the verification of the Mersenne number with exponent 333333367 and found it to be composite. The computations took a bit over a year on my home computer. I used CUDALucas for the computations. Please feel free to move this thread to wherever it's more appropriate. TheGuardian
 2019-05-05, 13:10 #2 Lorenzo     Aug 2010 Republic of Belarus 101100102 Posts https://www.mersenne.org/report_expo...p_lo=333333367 proof: M333333367 has a factor: 91333342559 [TF:1:64*:mfaktc 0.21 75bit_mul32_gs] found 1 factor for M333333367 from 2^ 1 to 2^64 (partially tested) [mfaktc 0.21 75bit_mul32_gs] Last fiddled with by Lorenzo on 2019-05-05 at 13:13
2019-05-05, 13:31   #3
paulunderwood

Sep 2002
Database er0rr

2×7×281 Posts

Quote:
 Originally Posted by TheGuardian The computations took a bit over a year on my home computer.

Quote:
 Originally Posted by Lorenzo M333333367 has a factor: 91333342559

Last fiddled with by paulunderwood on 2019-05-05 at 13:32

2019-05-05, 14:18   #4
TheGuardian

May 2019

2×3 Posts

Quote:
 Originally Posted by Lorenzo https://www.mersenne.org/report_expo...p_lo=333333367 proof: M333333367 has a factor: 91333342559 [TF:1:64*:mfaktc 0.21 75bit_mul32_gs] found 1 factor for M333333367 from 2^ 1 to 2^64 (partially tested) [mfaktc 0.21 75bit_mul32_gs]
Oh I wasn't aware of this website. Would have saved me quite some time :)

2019-05-05, 14:21   #5
TheGuardian

May 2019

2·3 Posts

Quote:
 Originally Posted by Lorenzo https://www.mersenne.org/report_expo...p_lo=333333367 proof: M333333367 has a factor: 91333342559 [TF:1:64*:mfaktc 0.21 75bit_mul32_gs] found 1 factor for M333333367 from 2^ 1 to 2^64 (partially tested) [mfaktc 0.21 75bit_mul32_gs]
PS. May I ask how these huge numbers came to be factored? Surely most deterministic algorithms would take ages to complete.

For instance, the exponent 333333367 is listed as "Factored", yet only 2 factors are known. Clearly, then the Mersenne number M333333367 is *not* factored. What am I missing?

2019-05-05, 14:56   #6
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

11,027 Posts

Quote:
 Originally Posted by TheGuardian PS. May I ask how these huge numbers came to be factored? Surely most deterministic algorithms would take ages to complete. For instance, the exponent 333333367 is listed as "Factored", yet only 2 factors are known. Clearly, then the Mersenne number M333333367 is *not* factored. What am I missing?
What you are missing is that in this context, "Factored" means that at least one prime factor is known.

2019-05-05, 16:16   #7
lukerichards

"Luke Richards"
Jan 2018
Birmingham, UK

25×32 Posts

Quote:
 Originally Posted by xilman What you are missing is that in this context, "Factored" means that at least one prime factor is known.
In this context, 'factored' is useful in so much as it tells us that the number is composite.

 2019-05-05, 17:27 #8 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 22·1,481 Posts Welcome to the hunt, TheGuardian. What gpu do you have? I hope you're running no earlier than the May 2017 version of CUDALucas. "Factored" in the GIMPS context means, at least one known prime factor found, and confirmed, so the exponent is ruled out as a possible Mersenne prime, no need to a) trial factor any further, b) P-1 factor, c) attempt LL primality test or PRP probable-prime test, d) double check whichever of LL or PRP were done in c preceding. Finding a factor is a welcome result, because it saves a lot of computing time. "Factored" is quite different from and a lower standard than "fully factored". To apply your gpu to needed work, and improve your chances of avoiding unneeded duplication of someone else's work, go to https://www.mersenne.org/manual_assignment/ or https://www.mersenne.org/manual_gpu_assignment/ To report the results, copy and paste into https://www.mersenne.org/manual_result/ You may find some of the content at https://www.mersenneforum.org/forumdisplay.php?f=154 useful background info. New user guidance draft https://www.mersenneforum.org/showpo...3&postcount=11 Specific to the many techniques used to make trial factoring fast, see https://www.mersenneforum.org/showpo...23&postcount=6 Last fiddled with by kriesel on 2019-05-05 at 17:49
2019-05-05, 17:33   #9
GP2

Sep 2003

258510 Posts

Quote:
 Originally Posted by TheGuardian For instance, the exponent 333333367 is listed as "Factored", yet only 2 factors are known. Clearly, then the Mersenne number M333333367 is *not* factored. What am I missing?
It's "factored" because at least one factor is known.

If we knew all the factors, then it would be "fully factored". Out of the tens of millions of Mersenne numbers we have tested, only 332 of them are fully factored (or strongly believed to be). This number slowly increases, since new factors are found all the time.

The largest exponent for which the Mersenne number is proven to be fully factored is 63,703. The largest exponent which is probably fully factored is 7,313,983.

Last fiddled with by GP2 on 2019-05-05 at 17:35

2019-05-05, 18:01   #10
lukerichards

"Luke Richards"
Jan 2018
Birmingham, UK

25×32 Posts

Quote:
 Originally Posted by GP2 The largest exponent which is probably fully factored is 7,313,983.
Probably factored meaning that the factors have passed PRP tests?

2019-05-05, 18:40   #11
M344587487

"Composite as Heck"
Oct 2017

2×3×5×29 Posts

Quote:
 Originally Posted by lukerichards Probably factored meaning that the factors have passed PRP tests?
Probably :P

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