Mersenne number factored (disbelievers are biting elbows)

[Batalov]

2357 is a pretty prime number itself. (2, 3, 5, 7, you know)
So it is doubly nice to have M2357 factored! Congrats, Ryan!

[axn]

Originally Posted by GP2

The cofactor will no doubt soon be certified prime on FactorDB.

Well, it is now...

[srow7]

something is wrong with the status of M2357.
F-ECM (factored)
P-PRP (probable prime) ?????
C-LL(verified)

https://www.mersenne.org/report_expo...exp_hi=&full=1

2019-04-05 ATH P-PRP M2357 is a probable prime.
2019-04-05 matzetoni P-PRP M2357/66747193058349253980250138299492944283449631375464079700189511 is a probable prime.
2019-04-05 Ryan Propper F-ECM Factor: 66747193058349253980250138299492944283449631375464079700189511

[ATH]

I did use the factor in the worktodo line, so it is:
M2357/66747193058349253980250138299492944283449631375464079700189511
that is PRP, but not sure why the history is wrong.

[Dr Sardonicus]

Congrats on completing another factorization! Something on the factordb page piqued my curiosity:

Bases checked 5, 7, 11, 13, 125, 127

It seemed weird that 125 was selected as a base, seeing as how the base 5 was checked, and 125 = 5^3.

[Batalov]

FDB allows users to manually check in any base (one just types in the "base" and the server runs it). Running funny bases, like 91 or 35 is not a faux pas per se. But 125 _after_ 5, - yeah, that's a bit silly.

[Madpoo]

Originally Posted by ATH

I did use the factor in the worktodo line, so it is:
M2357/66747193058349253980250138299492944283449631375464079700189511
that is PRP, but not sure why the history is wrong.

It's not wrong, it's just not displaying everything.

There is a frustrating amount of variations on how the JSON data was being formatted. Between the different builds of Prime95 and also gpuOwl, there was never really any agreement ahead of time on how it should look, so I've been playing catch-up with it.

For instance, the known factors may show up as a JSON array, or maybe as a value of comma separated numbers. Or maybe upper or lower case, or maybe it's another level deep, etc. LOL

George has settled on a (hopefully) final format in the latest builds of P95 but until we get the first example of something, I'm never really sure what it's going to look like.

Now that I see what a PRP looks like for a cofactor test, I can update the code that makes the raw result look pretty for the website. It did indeed change from:

"known-factors":"66747193058349253980250138299492944283449631375464079700189511"

to:

"known-factors":["66747193058349253980250138299492944283449631375464079700189511"]

Which is quite different. I had to go through the same thing with a non-prime result for cofactor PRP so it won't take me long to implement the new variation.

[GP2]

The 330th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M78737.

The 29-digit factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by ATH.

If certified prime, the cofactor would be a new record for Mersenne cofactors, beating the current M63703. However it would still be smaller than the Wagstaff prime with exponent 83339.

[petrw1]

Originally Posted by GP2

The 329th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M2357.

The 62-digit factor was found by Ryan Propper, and the PRP test on Primenet was done by matzetoni. The cofactor will no doubt soon be certified prime on FactorDB.

This is a semiprime, and its exponent p = 1 mod 4.

2557 Factored 92006001376648044276967530077499930523710420381051263551
2019-04-07 Ryan Propper F-ECM
Factor: 92006001376648044276967530077499930523710420381051263551

[paulunderwood]

Originally Posted by GP2

The 330th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M78737.

The 29-digit factor was found by Niels Mache Nextcloud, and the PRP test on Primenet was done by ATH.

If certified prime, the cofactor would be a new record for Mersenne cofactors, beating the current M63703. However it would still be smaller than the Wagstaff prime with exponent 83339.

My test of Neils' find:

time ./pfgw64 -k -f0 -od -q"(2^78737-1)/23714605956035916529/67059801476528402969297162417" | ../../coding/gwnum/lucasPRP - 1 2 78737 -1
                                               
Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real	0m2.558s
user	0m2.200s
sys	0m0.008s

[Batalov]

Originally Posted by petrw1

2557 Factored 92006001376648044276967530077499930523710420381051263551
2019-04-07 Ryan Propper F-ECM

...but disbelievers (that it is fully factored) are not fools