You are confusing the proof method (which you obviously have by definition for every number in the UTM database) and the "record" category.
The "record" category is only there to get the candidate submissions eligible for submission.

Adding "ECPP" tag to small numbers is in fact discouraged by the UTM admins.

The 324th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M32611[/M].

It hasn't been PRP tested on Primenet yet, but when I reported the new factor to Factordb, [URL="http://factordb.com/index.php?id=1000000000000032611"]it displayed FF[/URL].

As always, the Primo certification can be done by whoever claims it first.


Edit: actually, the results.txt file reported "Cofactor is a probable prime!" as well. I should have checked that first.

Will do proof

EDIT: Finished, uploaded and [URL="http://primes.utm.edu/primes/page.php?id=125463"]reported with UTM code c90[/URL].

My data has 286 prime exponent Mersenne numbers with prime or SPRP cofactors, which is a bit less, but I have a somewhat different definition of factors for Mersenne numbers than factordb.com uses.


The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.


The largest in my "completely factored" list are appended.


-- Will



M( 32531 )
M( 35339 )
M( 41263 )
M( 41521 )
M( 41681 )
M( 57131 )
M( 58199 )
M( 63703 )
M( 82939 )
M( 86137 )
M( 86371 )
M( 87691 )
M( 106391 )
M( 130439 )
M( 136883 )
M( 157457 )
M( 173867 )
M( 221509 )
M( 271211 )
M( 271549 )
M( 406583 )
M( 684127 )

For whatever reason, Factordb doesn't record PRPs above around 500k, and there is no way to report them. They list [url="http://factordb.com/index.php?query=M488441"]M488441[/url] as fully factored but not [url="http://factordb.com/index.php?query=M576551"]M576551[/url] or anything higher.

Your list is missing a number of recent discoveries, particularly at the high end. They are indicated in the bold links below.

However, new factors are continually being discovered for exponents of all sizes, each of which could potentially result in a new PRP. So to complete the list you also have to consider exponents smaller than 32531. For instance [M]M2789[/M] was fully factored a few months ago.

The full list is at [url]http://www.mersenne.ca/prp.php[/url], however unlike Factordb or your sourceforge file, only prime exponents are recorded. There are 324 entries. The ones above your threshold of 32531 are listed below:

32531
[B][M]32611[/M][/B]
35339
41263
41521
41681
[B][M]53381[/M][/B]
57131
58199
63703
82939
[B][M]84211[/M][/B]
86137
86371
87691
106391
130439
136883
[B][M]151013[/M][/B]
157457
173867
[B][M]174533[/M][/B]
[B][M]175631[/M][/B]
221509
[B][M]270059[/M][/B]
271211
271549
406583
[B][M]432457[/M][/B]
[B][M]440399[/M][/B]
[B][M]488441[/M][/B]
[B][M]576551[/M][/B]
[B][M]611999[/M][/B]
[B][M]675977[/M][/B]
684127
[B][M]696343[/M][/B]
[B][M]750151[/M][/B]
[B][M]822971[/M][/B]
[B][M]1010623[/M][/B]
[B][M]1168183[/M][/B]
[B][M]1304983[/M][/B]
[B][M]1629469[/M][/B]
[B][M]1790743[/M][/B]
[B][M]2327417[/M][/B]
[B][M]3464473[/M][/B]
[B][M]4187251[/M][/B]
[B][M]4834891[/M][/B]
[B][M]5240707[/M][/B]
[B][M]7080247[/M][/B]
[B][M]7313983[/M][/B]

[QUOTE=wedgingt;491888]The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.[/QUOTE]

This distinction isn't an issue for Mersenne numbers with prime exponents, since these cannot share factors with one another.

PRPtop has a subset of these, too: [URL]http://www.primenumbers.net/prptop/searchform.php?form=%282%5En-1%29%2F%3F&action=Search[/URL]
(this search result requires additional filtering before use)

[QUOTE=Batalov;491910]PRPtop has a subset of these, too: [URL]http://www.primenumbers.net/prptop/searchform.php?form=%282%5En-1%29%2F%3F&action=Search[/URL]
(this search result requires additional filtering before use)[/QUOTE]

Unfortunately that site no longer accepts new entries smaller than 30,000 digits, so more recent discoveries such as [M]M53381[/M] and [M]M84211[/M] are not listed.

It does include a handful of Mersenne numbers with non-prime exponents, but those all seem to be old discoveries from more than a decade ago.

Yes, indeed - there is a self-inflicted gap up to 30,000 decimal digits.

However, there is always a (very remote) chance that someone somewhere is still digging for unusual high PRPs (not to mention NooE) and would submit just to PRPtop. Who knows. I do cross-reference all sites every once in a while.

The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M51487[/M].

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.

[QUOTE=GP2;497937]The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M51487[/M].

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.[/QUOTE]

[CODE]time ./pfgw64 -k -f0 -od -q"(2^51487-1)/57410994232247/17292148963401772464767849635553" | ../../coding/gwnum/hybrid - 1 2 51487 -1

Testing (x + 1)^(n + 1) == 2 + 3 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 0m1.274s
user 0m1.332s
sys 0m0.008s
[/CODE]