[QUOTE=GP2;447216]All probable-prime cofactors for exponents 63703 and below have been proven prime (274 out of the 306), while all the larger ones are only (highly) probably prime.[/QUOTE]

The record for ECPP proof is about 31k digits ([url]http://primes.utm.edu/top20/page.php?id=27[/url]). That means the next four PRPs [C](M82939 - PRP-24938, M86137 - PRP-25896, M86371 - PRP-25984, M87691 - PRP-26371)[/C] are "provable" (with some serious time commitment.)

The 307th fully-factored-or-probably-fully-factored Mersenne number is [URL="http://www.mersenne.ca/exponent/25243"]M25243[/URL].

It has four factors plus a PRP cofactor. The fourth factor 449245236879223161338352589831 was found using P−1 stage 1 with B1=500000000.

This is within range of primality testing by Primo, if someone wants to tackle it.

[QUOTE=GP2;448486]The 307th fully-factored-or-probably-fully-factored Mersenne number is [URL="http://www.mersenne.ca/exponent/25243"]M25243[/URL].

It has four factors plus a PRP cofactor. The fourth factor 449245236879223161338352589831 was found using P−1 stage 1 with B1=500000000.

This is within range of primality testing by Primo, if someone wants to tackle it.[/QUOTE]

It will be a UTM submission: [URL="http://primes.utm.edu/top20/page.php?id=49"]top20[/URL] :smile:

Edit, I'll prove it prime with Primo -- is there someone I should co-credit?

Do we want PRP status of co-factors logged in primenet as well?

I'm not sure how mersenne.ca is updated? is it getting info from primenet via scripts running on primenet?

Does mersenne.ca contain other information missing from primenet besides the PRP information? Like extra factors for exponents besides the first one, that are not in primenet?

[QUOTE=ATH;448494]Do we want PRP status of co-factors logged in primenet as well?

I'm not sure how mersenne.ca is updated? is it getting info from primenet via scripts running on primenet?

Does mersenne.ca contain other information missing from primenet besides the PRP information? Like extra factors for exponents besides the first one, that are not in primenet?[/QUOTE]

Primenet does not store any information about which exponents are fully-factored or probably-fully-factored. It should, or at least we should make sure that fully-factored exponents are eliminated from consideration for any further factoring by ECM or other method.

mprime/Prime95 can do PRP testing, but it does not send the results to Primenet, nor can these results be manually submitted to Primenet. These results have to be manually submitted to Mersenne.ca, at [url]http://www.mersenne.ca/index.php?submitresults=1[/url]

Mersenne.ca is the central repository for PRP information on Mersenne exponents, with the full list at [url]http://www.mersenne.ca/prp.php[/url]

All of the PRP exponents up to and including M63,703 have had their cofactors certified prime with Primo or some other means. All the higher exponents are only probably-fully-factored, albeit with very high confidence.

Ranges for PRP testing can be reserved at [url]http://www.mersenne.ca/prp.php?assigned_distribution=1[/url] by clicking on the blue links and then clicking on the button in the resulting page. However, that page does not really document clearly that results need to be submitted at [url]http://www.mersenne.ca/index.php?submitresults=1[/url]

Mersenne.ca pulls updates daily from Primenet. Both of these sites should have identical information about residues and factors, including second and higher factors. A few months ago, a few dozen inconsistencies were discovered between the two databases, but those were reconciled and presumably there is no longer an issue.

One difference is that Mersenne.ca has factors data for exponents up to 4.29 billion, whereas Primenet only stores factors data for exponents up to 1.00 billion.

[QUOTE=paulunderwood;448489]It will be a UTM submission: [URL="http://primes.utm.edu/top20/page.php?id=49"]top20[/URL] :smile:

Edit, I'll prove it prime with Primo -- is there someone I should co-credit?[/QUOTE]

[URL="http://primes.utm.edu/primes/page.php?id=122574"]Submission[/URL] to The Prime Pages.

I submitted the certificate to FactorDB. Can some please provide me with a link to it so I can include the link in TPP database :smile:

[QUOTE=paulunderwood;448489]
... is there someone I should co-credit?[/QUOTE]
GP2?

[QUOTE=Batalov;448667]GP2?[/QUOTE]

No need...

I have added a link at TPP to the cofactor certificate at FactorDB. Now [url]http://www.mersenne.ca/exponent/25243[/url] can be updated from "probable prime" to "prime"

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