[QUOTE=Jayder;448936]Good going. If it's alright, I'd like to do the certificate for this one. It will be done within the day.[/QUOTE]

Well, I guess you called dibs.

And the hits just keep on coming:

[URL="http://www.mersenne.ca/exponent/4834891"]M4834891[/URL]/1701881633/70659688575577 is a probable prime

This is the 309th fully-or-probably-fully factored Mersenne exponent, and the second largest after M5240707.

This is an unexpected flurry of new PRP results.

The factors were discovered long ago, but now the wavefront of PRP testing has reached the 4.8M range...

[QUOTE=GP2;449044]
[URL="http://www.mersenne.ca/exponent/4834891"]M4834891[/URL]/1701881633/70659688575577 is a probable prime
.[/QUOTE]

FWIW:

[CODE]time ../../coding/gwnum/lucasPRP M4834891-cofactor 1 2 4834891 -1
Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real 64m3.983s
user 228m46.452s
sys 4m39.080s[/CODE]

[URL="http://www.mersenneforum.org/showpost.php?p=435694&postcount=14"]Reference program[/URL] :geek:

[QUOTE=GP2;448932]The 308th known probably-fully-factored Mersenne exponent is [URL="http://www.mersenne.ca/exponent/25933"]M25933[/URL].

It has three factors plus the PRP cofactor, and its latest 40-digit factor 5589137403017310421606050379256829183569 was found using P-1 with B1=500000000, B2=19081568754210, using mprime for stage 1 and gmp-ecm for stage 2.

Like the last time, this needs a Primo certificate.[/QUOTE]
Forgot to post this yesterday: [url]http://factordb.com/index.php?id=1100000000886495500[/url]

Is it suggested that I submit this to the Prime Pages? I will have to make an account and figure it out if so.

[QUOTE=Jayder;449055]Forgot to post this yesterday: [url]http://factordb.com/index.php?id=1100000000886495500[/url]

Is it suggested that I submit this to the Prime Pages? I will have to make an account and figure it out if so.[/QUOTE]

Yes. It is a top20 proven Mersenne cofactor :smile:

[URL="http://factordb.com/index.php?query=2%5E53381-1"]factordb is showing that M53381 is fully-factored[/URL]

As of this writing, it has [URL="http://www.mersenne.ca/exponent/53381"]not been tested yet at mersenne.ca[/URL]

It has three factors plus the PRP cofactor. I found the third factor a couple of days ago using ECM. This is the 310th known fully-factored or probably-fully-factored Mersenne exponent.

This one will be a bit challenging to certify primality. Who wants to try it?

[QUOTE=GP2;449724][URL="http://factordb.com/index.php?query=2%5E53381-1"]factordb is showing that M53381 is fully-factored[/URL]

As of this writing, it has [URL="http://www.mersenne.ca/exponent/53381"]not been tested yet at mersenne.ca[/URL]

It has three factors plus the PRP cofactor. I found the third factor a couple of days ago using ECM. This is the 310th known fully-factored or probably-fully-factored Mersenne exponent.

This one will be a bit challenging to certify primality. Who wants to try it?[/QUOTE]

I'll pick it up. It will take about four weeks on a 6 core 1090T. Until then... :smile:

[QUOTE=GP2;449724]As of this writing, it has [URL="http://www.mersenne.ca/exponent/53381"]not been tested yet at mersenne.ca[/URL][/QUOTE]

It is now.

Mersenne.ca is showing that M[URL="http://www.mersenne.ca/exponent/84211"]84211[/URL]/1347377/31358793176711980763958121/3314641676042347824169591561 is a probable prime.

It is the 311th known fully-factored or probably-fully-factored Mersenne exponent. The third factor was discovered a few days ago, the results.txt actually reported "Cofactor is a probable prime!" but I didn't notice it at the time.

It is a bit too large for primality certification to be feasible in a reasonable amount of time. Note that certification of the next-lower M82939 has not been attempted yet, as far as I know. The largest certified fully-factored exponent is M63703.

There are now five known probably-fully-factored Mersenne exponents in the 80k range (82939, 84211, 86137, 86371, 87691), not to mention the prime M86243, but none in the 70k range.

[QUOTE=GP2;454160]Mersenne.ca is showing that M[URL="http://www.mersenne.ca/exponent/84211"]84211[/URL]/1347377/31358793176711980763958121/3314641676042347824169591561 is a probable prime.

It is the 311th known fully-factored or probably-fully-factored Mersenne exponent. The third factor was discovered a few days ago, the results.txt actually reported "Cofactor is a probable prime!" but I didn't notice it at the time.

It is a bit too large for primality certification to be feasible in a reasonable amount of time. Note that certification of the next-lower M82939 has not been attempted yet, as far as I know. The largest certified fully-factored exponent is M63703.

There are now five known probably-fully-factored Mersenne exponents in the 80k range (82939, 84211, 86137, 86371, 87691), not to mention the prime M86243, but none in the 70k range.[/QUOTE]

On a many core/socket system, these can be proved in a "reasonable amount of time", because a proof with ECPP (using Primo) is [URL="https://en.wikipedia.org/wiki/Embarrassingly_parallel"]embarrassingly parallel[/URL].

[QUOTE=paulunderwood;454164]On a many core/socket system, these can be proved in a "reasonable amount of time", because a proof with ECPP (using Primo) is [URL="https://en.wikipedia.org/wiki/Embarrassingly_parallel"]embarrassingly parallel[/URL].[/QUOTE]

Well, feel free to tackle it after M53381... :smile: although M82939 might have priority.

Odd that no PRPs were found in the 70k range or the upper half of 60k. I did find factors there but no PRPs resulted.