Mersenne number factored (disbelievers are biting elbows)

[Prime95]

Originally Posted by GP2

The others are only (very) probably-fully-factored. The Primenet database should probably distinguish between the two cases, as Mersenne.ca already does.

The database does distinguish but needs to be updated manually as the server does not store certificates.

[VictordeHolland]

Sorry if this is offtopice, but I wanted to try PRIMO as I've never used it before.

I tried it on a (Sandy-Bridge based) 1x Xeon 2620 (6c12t, 2GHz-ish) with 16GB ECC RAM and Ubuntu 16.04 LTS
I used 12 threads and sieve 5000 - 25 bits (is there a guide on what parameters to use? I couldn't find it in the readme or FAQ?)

So I tried some of the standard input files and added M8243cofactor as an exercise
10^55+21 - 0.13s
10^700+7 - 12.57s
10^999+7 - 61s
M8243-cofactor - 1826s

They were all prime (as known/expected) and I got a bunch of files now
.in (the Input, that makes sense)
.wr (Work Report?)
.cr (Certificate Report?)
.out (Primality Certificate?)
So which ones do you need to upload/report in case it is a new test and where do you upload them?

[paulunderwood]

Originally Posted by VictordeHolland

Sorry if this is offtopice, but I wanted to try PRIMO as I've never used it before.

I tried it on a (Sandy-Bridge based) 1x Xeon 2620 (6c12t, 2GHz-ish) with 16GB ECC RAM and Ubuntu 16.04 LTS
I used 12 threads and sieve 5000 - 25 bits (is there a guide on what parameters to use? I couldn't find it in the readme or FAQ?)

So I tried some of the standard input files and added M8243cofactor as an exercise
10^55+21 - 0.13s
10^700+7 - 12.57s
10^999+7 - 61s
M8243-cofactor - 1826s

They were all prime (as known/expected) and I got a bunch of files now
.in (the Input, that makes sense)
.wr (Work Report?)
.cr (Certificate Report?)
.out (Primality Certificate?)
So which ones do you need to upload/report in case it is a new test and where do you upload them?

My test of M8243-cofactor took 1400 seconds on a o/c 4770k. I uploaded the certificate -- yes the .out file -- to http://www.factordb.com/result.php.

I used the default parameters, but on big jobs I max them out.

[VictordeHolland]

Originally Posted by paulunderwood

My test of M8243-cofactor took 1400 seconds on a o/c 4770k. I uploaded the certificate -- yes the .out file -- to http://www.factordb.com/result.php.

I used the default parameters, but on big jobs I max them out.

Thx!

Yeah, my time seems to be what is expected, considering it is 2 generations older and the GHz*cores is lower than yours. Xeon 2620 (6c*2.3GHz=13.8) vs. your 4770k (4c*4GHz??=16?).

[James Heinrich]

Originally Posted by GP2

Mersenne.org is now listing PRP residues in a separate Cofactor PRP section. Excellent.

Mersenne.ca now automatically imports PRP results from mersenne.org (overnightly), and the exponent details page has an additional section with the PRP logs from PrimeNet.

[GP2]

The 318th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M20521.

I found the most recent factor, and Oliver Kruse did the PRP test.

As usual, needs a Primo certificate, if anyone wants to do it.


As is usually the case for small exponents, the ECM curve that found the factor actually output "Cofactor is a probable prime", although I didn't notice this until after the fact.

So the ECM code automatically does a PRP test, at least for small exponents, and calculates a residue. Perhaps in future versions it could send that residue result straight to the database.

[paulunderwood]

Originally Posted by GP2

The 318th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M20521.

I found the most recent factor, and Oliver Kruse did the PRP test.

As usual, needs a Primo certificate, if anyone wants to do it.

I'm certifying it now...

[paulunderwood]

Certification of the M20521 cofactor is complete. This prime makes it into the top20 Mersenne cofactors.

[Dr Sardonicus]

I notice something amusing WRT fully-factored Mp's whose last factor is a PRP-cum-certified-prime: The tables, e.g.for 20521 or even 397 list all but the last factor as "known prime factors" but describe the remaining cofactor as a "certified-prime." In the case of 397, this affects the description in the table of Top Mersenne exponents with the most known factors, which says M397 has only 8 known prime factors! Since the last factor is only 31 decimal digits, the primality would seem to beyond cavil...

[GP2]

Originally Posted by Dr Sardonicus

I notice something amusing WRT fully-factored Mp's whose last factor is a PRP-cum-certified-prime: The tables, e.g.for 20521 or even 397 list all but the last factor as "known prime factors" but describe the remaining cofactor as a "certified-prime." In the case of 397, this affects the description in the table of Top Mersenne exponents with the most known factors, which says M397 has only 8 known prime factors! Since the last factor is only 31 decimal digits, the primality would seem to beyond cavil...

And M11 has only "one" known factor, even though it's actually the product of 23 × 89.

For the sake of consistency we always omit that final cofactor, which is usually both enormous and composite.

[James Heinrich]

Originally Posted by Dr Sardonicus

In the case of 397, this affects the description in the table of Top Mersenne exponents with the most known factors, which says M397 has only 8 known prime factors! Since the last factor is only 31 decimal digits, the primality would seem to beyond cavil...

There are indeed 9 factors for M397, the smallest 8 of which are listed on the exponent page, the last one (6597485910270326519900042655193) is only shown on demand on the PRP page.

I have updated the many-factors page to take these kind of PRP last-factors into account, the affected exponents are shown in red.
And yes, in many cases with smaller exponents the percentage-known won't quite reach 100% due to rounding.