[QUOTE=GP2;454165]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.[/QUOTE]

I decline your offer of testing those hefty numbers :wink:

I have completed the certificate of the M53381 cofactor and have submitted it to both [URL="http://primes.utm.edu/primes/page.php?id=123121"]UTM's The Prime Pages[/URL] and factordb. Please update your records :smile:

[QUOTE=paulunderwood;454500]I decline your offer of testing those hefty numbers :wink:

I have completed the certificate of the M53381 cofactor and have submitted it to both [URL="http://primes.utm.edu/primes/page.php?id=123121"]UTM's The Prime Pages[/URL] and factordb. Please update your records :smile:[/QUOTE]
Seems like its already updated, rank 4 on the Mersenne cofactor list, congrats!

[quote][INDENT][URL="http://primes.utm.edu/top20/page.php?id=27"]Elliptic Curve Primality Proof[/URL] (archivable [URL="http://primes.utm.edu/top20/home.php#archivable"]*[/URL]) Prime on list: [B]no[/B], rank [B]41[/B]
Subcategory: "ECPP"

[URL="http://primes.utm.edu/top20/page.php?id=49"]Mersenne cofactor[/URL] (archivable [URL="http://primes.utm.edu/top20/home.php#archivable"]*[/URL]) Prime on list: [B]yes[/B], rank [B]4[/B]
Subcategory: "Mersenne cofactor"

[/INDENT][/quote]

The 312th fully-factored or probably-fully-factored Mersenne exponent is [URL="http://www.mersenne.ca/exponent/175631"]M175631[/URL]

It has two smaller factors plus a PRP cofactor. The second factor was found by user TJAOI on March 3. I'm not sure who ran the PRP test.

Someone has been running hundreds of ECM curves on [URL="https://www.mersenne.org/report_exponent/?exp_lo=53381&exp_hi=&full=1&ecmhist=1"]M53381[/URL] in the past few days, even though it has been known to be probably-fully-factored since December, and certified fully-factored a few days ago... hmmm...

Probably-fully-factored and fully-factored exponents ought to be removed from the ECM report listings. Some already have been but some haven't. Right now, [URL="https://www.mersenne.org/report_ecm/?txt=0&ecm_lo=1&ecm_hi=1&ecmnof_lo=53300&ecmnof_hi=53400"]53381 still appears there[/URL].

[QUOTE=GP2;454567]Someone has been running hundreds of ECM curves on [URL="https://www.mersenne.org/report_exponent/?exp_lo=53381&exp_hi=&full=1&ecmhist=1"]M53381[/URL] in the past few days ...[/QUOTE]
The proverbial disbelievers, right? :rolleyes:

[QUOTE=Batalov;454579]The proverbial disbelievers, right? :rolleyes:[/QUOTE]

...and it wasn't me :leaving:

[M]M12569[/M] is the 313th known fully-factored or probably-fully-factored Mersenne number.

Anyone want to run Primo on it?

[QUOTE=GP2;456219][M]M12569[/M] is the 313th known fully-factored or probably-fully-factored Mersenne number.

Anyone want to run Primo on it?[/QUOTE]

:jcrombie: I will do it

[QUOTE=paulunderwood;456225]:jcrombie: I will do it[/QUOTE]

Done: [URL="http://www.factordb.com/index.php?id=1100000000919047896"]factorDB entry[/URL]. It is too small for UTM's top20 Mersenne cofactors. :cool:

[URL="https://www.mersenne.ca/exponent/174533"]M174533[/URL] is the 314th known Mersenne number probably fully factored.

Been a long time since I fiddled with the M-cofactors, but a gander at the Top 20 page shows me that the largest 5 I posted (as PRPs) to the old mersenne mailing list in October 1997 have all been proven in recent years.

p
14561 8074991336582835391. p4365
17029 418879343. p5118
28759 226160777. p8649
28771 104726441. p8653
32531 65063.25225122959. p9778

Not to seem greedy-for-credit, but a link to the aforementioned mailing-list posting might be in order for the References section. I will fwd link to this post to Chris C. after it goes up.