Fully factored

[mattmill30]

Is there a "fully TF'd" list of exponents on mersenne.ca?

[VBCurtis]

Define "fully TF'ed". Do you mean fully factored?

[mattmill30]

Yes, fully factored

[Siegmund]

This would be an interesting list to see.

I suspect there are very few large exponents on the list -- finding one 60- or 70-bit factor of a million-digit number leaves a very large nut to crack.

[VBCurtis]

Check the top-5000 primes page for mersenne cofactors.
I assume there is a prp version of that page too with larger cofactors too big for ECPP just yet- perhaps someone could aim me the right direction?

[Batalov]

A superset of the PRPs is here.

There are some (2^ap-1)/(2^a-1)/f as you can see.
If you replace "?" with "f", then you could miss some cofactors that were submitted like (2^p-1)/f₁/f₂

[paulunderwood]

Yes: top 20 Mersenne cofactors (proven).

There are some outstanding ones less than Primo's 35k digit limit.

Here the reported gigantic PRPs -- I dare say Henri's list is out of date, in that some PRPs are proven primes.

I am currently proving a ~15k digit Mersenne cofactor -- ETA less than a month form now.

[GP2]

Originally Posted by paulunderwood

Here the reported gigantic PRPs -- I dare say Henri's list is out of date, in that some PRPs are proven primes.

It also has the problem that the formats of the entries are not normalized, but are simply stored however they were reported. For example M1790743 does not appear in the link you gave because it is stored as (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) and therefore doesn't match the pattern (2^p-1)/n

Similarly M4834891, M822971, M750151, M696343, M675977, M576551, M488441, M440399, M270059, M157457, M41681 are missing. All of these do appear when you click the "The Full PRP Top" (on the first page from 1 to 250, or subsequent pages).

[GP2]

Originally Posted by mattmill30

Is there a "fully TF'd" list of exponents on mersenne.ca?

Yes, here is the complete list. There are currently 310 fully-factored or probably-fully-factored exponents, in addition to the Mersenne primes themselves which are certainly also fully factored.

Only 63703 and smaller are certified and proven to be fully factored, the higher exponents have a probable-prime (PRP) cofactor, albeit with extremely high confidence.

[Xyzzy]

Originally Posted by GP2

Yes, here is the complete list. There are currently 310 fully-factored or probably-fully-factored exponents, in addition to the Mersenne primes themselves which are certainly also fully factored.

Only 63703 and smaller are certified and proven to be fully factored, the higher exponents have a probable-prime (PRP) cofactor, albeit with extremely high confidence.

A lot of those PRP cofactors could be tested easily. We wonder why nobody has done that.

[GP2]

Originally Posted by Xyzzy

A lot of those PRP cofactors could be tested easily. We wonder why nobody has done that.

I imagine it's harder than you think.

The record for Primo is 34093 decimal digits, which took 14 months with 48 cores, plus 200 additional days with 6 cores, by none other than Paul Underwood.

Based on that, M106391 (with a cofactor of 32010 decimal digits) is the largest Mersenne exponent that could feasibly be fully factored at the present time. The next smallest is M130439, with a cofactor of 39261 decimal digits.