Mersenne number factored (disbelievers are biting elbows)

[Dr Sardonicus]

Originally Posted by ATH

Ryan Propper found another factor and another PRP #356: M3917

I'm curious. Usually when a cofactor tests as a PRP, the residue is listed as

PRP_PRP_PRP_PRP_

But here, although the history says the remaining cofactor is a probable prime, the PRP cofactor residue is a hex value with, I presume, the last few digits obscured pending confirmation...

[ATH]

Originally Posted by Dr Sardonicus

I'm curious. Usually when a cofactor tests as a PRP, the residue is listed as

PRP_PRP_PRP_PRP_

But here, although the history says the remaining cofactor is a probable prime, the PRP cofactor residue is a hex value with, I presume, the last few digits obscured pending confirmation...

Yeah, that is strange I had not noticed, since it was spamming my results.txt with PRP. It was on an AWS instance, and I only noticed it by coincidence, because I was upgrading it to 30.6b4.

Now I ran it again and unintentionally double checked my own result, now it shows as PRP. But PRP-CF usually do not have hidden or fake residues?
I'm not sure why it used type 1 PRP test, here in the 2nd manual test I specifically told it to do a type 5 test.

Someone else please double check it as well.

[GP2]

Originally Posted by ATH

Someone else please double check it as well.

Like Ryan's other recent factor discoveries, the factor got reported almost immediately to FactorDB (by Ryan himself?), and the cofactor is usually already certified prime there before the first PRP test completes on PrimeNet.

FactorDB link

[LaurV]

Wow, 61 digits? That's a beast! Congrats Ryan!

[Dr Sardonicus]

A 61 decimal digit factor winkled out. Amazing!

Whatever the problem was with the PRP cofactor residue, it's been fixed. Two tests show a residue of PRP_PRP_PRP_PRP_

And, as previously noted, the cofactor is already certified prime. Another fully-factored Mersenne composite!

[GP2]

There are now 357 known Mersenne numbers with prime exponent that are composite and either fully factored or probably fully factored.

The most recent is M4021. Its final factor (66 digits) was found by Ryan Propper on 2021-05-19 and the PRP test was done by user "mnd9".

FactorDB link

The cofactor was already certified prime yesterday on FactorDB.

[tuckerkao]

Just finished the PRP-CF of M3769231 and M5078387, looks like Ben Delo will certify both exponents like last time.

Wondering whether anyone has a P-PRP cofactor with the exponent size over 1M on the record?

[masser]

Originally Posted by tuckerkao

Just finished the PRP-CF of M3769231 and M5078387, looks like Ben Delo will certify both exponents like last time.

Wondering whether anyone has a P-PRP cofactor with the exponent size over 1M on the record?

See post 519 of this thread.

[Dr Sardonicus]

Originally Posted by masser

See post 519 of this thread.

That would be this post.

See also the next post to the thread, this post.

(The PRP cofactor (2^10443557-1)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site)

[masser]

Originally Posted by Dr Sardonicus

That would be this post.

See also the next post to the thread, this post.

(The PRP cofactor (2^10443557-1)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site)

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

[tuckerkao]

Originally Posted by Dr Sardonicus

(The PRP cofactor (2^10443557-1)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site)

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?