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

[url]https://www.mersenne.org/report_exponent/?exp_lo=333333367[/url]

:groan:

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]

[Quote=TheGuardian]
The computations took a bit over a year on my home computer.
[/quote]


[QUOTE=Lorenzo]

M333333367 has a factor: 91333342559 [/QUOTE]

:shock: :nocomment: :rofl: :missingteeth: :not prime:

[QUOTE=Lorenzo;515826][url]https://www.mersenne.org/report_exponent/?exp_lo=333333367[/url]

:groan:

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][/QUOTE]

Oh I wasn't aware of this website. Would have saved me quite some time :)

[QUOTE=Lorenzo;515826][url]https://www.mersenne.org/report_exponent/?exp_lo=333333367[/url]

:groan:

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][/QUOTE]

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?

[QUOTE=TheGuardian;515836]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?[/QUOTE]What you are missing is that [B]in this context,[/B] "Factored" means that at least one prime factor is known.

[QUOTE=xilman;515838]What you are missing is that [B]in this context,[/B] "Factored" means that at least one prime factor is known.[/QUOTE]

In this context, 'factored' is useful in so much as it tells us that the number is composite.

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 [URL]https://www.mersenne.org/manual_assignment/[/URL] or [URL]https://www.mersenne.org/manual_gpu_assignment/[/URL]
To report the results, copy and paste into [URL]https://www.mersenne.org/manual_result/[/URL]
You may find some of the content at [URL]https://www.mersenneforum.org/forumdisplay.php?f=154[/URL] useful background info.
New user guidance draft [URL]https://www.mersenneforum.org/showpost.php?p=514003&postcount=11[/URL]
Specific to the many techniques used to make trial factoring fast, see [URL]https://www.mersenneforum.org/showpost.php?p=508523&postcount=6[/URL]

[QUOTE=TheGuardian;515836]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?[/QUOTE]

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 [URL="https://www.mersenne.ca/prp.php"]332 of them[/URL] 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 [M]63,703[/M]. The largest exponent which is probably fully factored is [M]7,313,983[/M].

[QUOTE=GP2;515850]The largest exponent which is probably fully factored is [M]7,313,983[/M].[/QUOTE]

Probably factored meaning that the factors have passed PRP tests?

[QUOTE=lukerichards;515851]Probably factored meaning that the factors have passed PRP tests?[/QUOTE]
Probably :P