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-   -   Mersenne number factored (disbelievers are biting elbows) (https://www.mersenneforum.org/showthread.php?t=19407)

axn 2022-06-04 02:03

[QUOTE=GP2;607086]M[M]245107[/M] is a probable semi-prime.

Factor found by Sid & Andy. Test by user SRJ2877.[/QUOTE]

Congrats @petrw1. I believe this is the first "confirmed kill" for the "low" project

tuckerkao 2022-06-04 03:47

[QUOTE=GP2;607086]M[M]245107[/M] is a probable semi-prime.

Factor found by Sid & Andy. Test by user SRJ2877.[/QUOTE]
Does the PRP-co-factor need to be run by other users as well or not to confirm? If yes, how long will it take? Is there perhaps an upper limit on the exponent size which the alternative program can reach up to?

[QUOTE=paulunderwood;606324]Congrats to Ryan for proving the cofactor of M78737 using FastECPP.[/QUOTE]
Not sure whether FastECPP runs like LL or not.

There were 2 users on M[M]10443557[/M]

petrw1 2022-06-04 05:00

[QUOTE=GP2;607086]M[M]245107[/M] is a probable semi-prime.

Factor found by Sid & Andy. Test by user SRJ2877.[/QUOTE]

OMG I'm almost famous ... :redface:

tuckerkao 2022-06-04 05:06

[QUOTE=petrw1;607106]OMG I'm almost famous ... :redface:[/QUOTE]
I thought you were Wayne. Is Sid & Andy or SRJ2877 your testing account or are they your followers?

[QUOTE=axn;607101]Congrats @petrw1. I believe this is the first "confirmed kill" for the "low" project[/QUOTE]
Does the project manager get the credit if 1 of the follower users made the discovery?

axn 2022-06-04 05:24

"Sid & Andy" is petrw1's GIMPS username

ixfd64 2022-06-04 06:54

[QUOTE=tuckerkao;607105]Does the PRP-co-factor need to be run by other users as well or not to confirm? If yes, how long will it take? Is there perhaps an upper limit on the exponent size which the alternative program can reach up to?[/QUOTE]

Yes, but it is not necessary to re-run the whole test as we can also generate PRP proofs for cofactors. Verifying a proof is much faster.

mathwiz 2022-06-04 10:54

[QUOTE=tuckerkao;607105]Not sure whether FastECPP runs like LL or not.[/QUOTE]

I have no idea what you mean by "runs like". But... no.

FastECPP is a completely different algorithm and proof method. It can be distributed among many machines using MPI. The algorithm itself has nothing to do with LL testing.

GP2 2022-07-03 19:04

M[M]12,720,787[/M] has been reported fully factored. The PRP test was done by user Funky Waddle.

This would be a new record, eclipsing M[M]10,443,557[/M] from July 2020.

masser 2022-10-20 02:22

[QUOTE=GP2;608936]M[M]12,720,787[/M] has been reported fully factored. The PRP test was done by user Funky Waddle.

This would be a new record, eclipsing M[M]10,443,557[/M] from July 2020.[/QUOTE]

This result doesn't appear to have been reported to [URL="http://www.primenumbers.net/prptop/prptop.php"]http://www.primenumbers.net/prptop/prptop.php[/URL]. Has anyone tried to submit this PRP?

paulunderwood 2022-10-30 13:05

Congrats to Serge for proving with CM (ECPP) the [URL="https://primes.utm.edu/primes/page.php?id=134494"]cofactor of M87691[/URL]. :tu:

paulunderwood 2022-11-25 04:57

I have just made a submission to The Prime Pages and uploaded the certificate do factorDB for the [URL="https://primes.utm.edu/primes/page.php?id=134576"]M174533 cofactor[/URL]. :flex:

paulunderwood 2022-12-07 20:47

[QUOTE=paulunderwood;618447]I have just made a submission to The Prime Pages and uploaded the certificate do factorDB for the [URL="https://primes.utm.edu/primes/page.php?id=134576"]M174533 cofactor[/URL]. :flex:[/QUOTE]

The certificate has been verified by factorDB. Now [url]https://www.mersenne.ca/prp.php[/url] needs to be updated.

Mark Rose 2022-12-07 21:27

[QUOTE=paulunderwood;619196]The certificate has been verified by factorDB. Now [url]https://www.mersenne.ca/prp.php[/url] needs to be updated.[/QUOTE]

M43 and higher are also missing.

James Heinrich 2022-12-09 17:57

[QUOTE=paulunderwood;619196]The certificate has been verified by factorDB.
Now [url]https://www.mersenne.ca/prp.php[/url] needs to be updated.[/QUOTE]Sorry, I was offline for 4 days, but it seems my adminion has updated it in my absence.

[QUOTE=Mark Rose;619197]M43 and higher are also missing.[/QUOTE]Kinda-sorta... the PRP section is limited to 30M so you didn't see any larger Mersenne Primes. The limit remains in place, but I'm now always including the Primes in the list to avoid confusion.

Andrew Usher 2022-12-10 17:20

It may now be limited to 30M, but practically that's of no importance, since if a PRP larger than that is discovered you'll find a way to include it, I imagine.

I have calculated the density of PRP cofactors that should be expected (by the 1/n law) and it agrees satisfactorily with what's actually been found: their density should exceed that expected for Mersenne primes by the ratio

log(eff. factoring level)/log(4p)

where the effective factoring limit is (logarithmically) averaged over all exponents, so increasing it is easiest by further work on _factored_ exponents, in particular, running quick P-1 on exponents that have had none is the fastest way to increase it and also (which is equivalent) the fastest way to find factors. Whether anyone should do this depends on the value placed on PRPs.

Andrew Usher 2022-12-12 13:23

I should have clarified that my formula is fundamentally the probability of PRP after each factor found; averaging over all exponents in a range gives a density of PRPs. 'Quick' P-1 in that form of search would be nearly the Primenet standard on mersenne.ca (for B1), as it makes sense to always go to that level before a PRP; regardless of how many factors are known, the probability of another is the same.


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