Mersenne number factored (disbelievers are biting elbows)

[paulunderwood]

Originally Posted by tuckerkao

What test will be needed to confirm the probable prime from the cofactor of M10443557? Is there 1 doable test like LL to the regular PRP?

The short answer is "no!". See https://primes.utm.edu/prove/

[Dr Sardonicus]

Originally Posted by masser

I would like young Tucker to do some of the legwork himself.

So would I. But if he were willing to do legwork himself, he would not have posted his query. I posted the links for the benefit of others. Back when I was a new user, I was advised to use "show single post" in referring to previous posts. Locating the page with a given post number in a long thread can be tedious.

But, just for fun, I will mention that two smaller p > 1000000 for which M_p has a large PRP cofactor are mentioned on this Forum, somewhere in this thread, which is a predecessor to the present one. That thread is much shorter than this one.

[tuckerkao]

Originally Posted by Dr Sardonicus

But, just for fun, I will mention that two smaller p > 1000000 for which M_p has a large PRP cofactor are mentioned on this Forum, somewhere in this thread, which is a predecessor to the present one. That thread is much shorter than this one.

I saw 4 of them inside that thread: M4187251, M4834891, M5240707, M7080247. Those are the 4 predecessors of M10443557 which is the current largest known P-PRP-CF.

I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.

The total quantity is scarce enough that qualifies to be the Mersenne treasures of the discoverers.

[chalsall]

Originally Posted by tuckerkao

I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.

That sounds like it would be better under the Wiki.

Why don't you step up, and curate that? Might reduce the noise here on the Forum.

Just asking...

[axn]

Originally Posted by tuckerkao

I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.

https://www.mersenne.ca/prp.php

[paulunderwood]

Congrats to Gelly (Robert Gelhar) for proving prime the co-factor of 2^106391-1

[paulunderwood]

Congrats to Ryan for proving the cofactor of M78737 using FastECPP.

[paulunderwood]

M86137 cofactor has been certified prime by yours truly.

[a1call]

Congrats for proving a now P25924 prime.

[GP2]

M245107 is a probable semi-prime.

Factor found by Sid & Andy. Test by user SRJ2877.

[axn]

Originally Posted by GP2

M245107 is a probable semi-prime.

Factor found by Sid & Andy. Test by user SRJ2877.

Congrats @petrw1. I believe this is the first "confirmed kill" for the "low" project