20190505, 11:38  #1 
May 2019
6_{8} 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 
20190505, 13:10  #2 
Aug 2010
Republic of Belarus
10110010_{2} 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 20190505 at 13:13 
20190505, 13:31  #3  
Sep 2002
Database er0rr
2×7×281 Posts 
Quote:
Quote:
Last fiddled with by paulunderwood on 20190505 at 13:32 

20190505, 14:18  #4  
May 2019
2×3 Posts 
Quote:


20190505, 14:21  #5  
May 2019
2·3 Posts 
Quote:
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? 

20190505, 14:56  #6  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
11,027 Posts 
Quote:


20190505, 16:16  #7 
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}×3^{2} Posts 

20190505, 17:27  #8 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{2}·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) P1 factor, c) attempt LL primality test or PRP probableprime 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 20190505 at 17:49 
20190505, 17:33  #9  
Sep 2003
2585_{10} Posts 
Quote:
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 20190505 at 17:35 

20190505, 18:40  #11 
"Composite as Heck"
Oct 2017
2×3×5×29 Posts 

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