20180405, 17:05  #419 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7×23×61 Posts 
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. 
20180715, 18:01  #420 
Sep 2003
5×11×47 Posts 
The 324th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M32611.
It hasn't been PRP tested on Primenet yet, but when I reported the new factor to Factordb, it displayed FF. 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. Last fiddled with by GP2 on 20180715 at 18:06 
20180715, 18:46  #421 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7·23·61 Posts 
Last fiddled with by Batalov on 20180717 at 18:43 Reason: finished yesterday 
20180716, 05:44  #422 
"Will Edgington"
Nov 2010
Utah, USA
2^{3}×3 Posts 
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 ) 
20180716, 14:14  #423 
Sep 2003
5·11·47 Posts 
For whatever reason, Factordb doesn't record PRPs above around 500k, and there is no way to report them. They list M488441 as fully factored but not M576551 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 M2789 was fully factored a few months ago. The full list is at http://www.mersenne.ca/prp.php, 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 32611 35339 41263 41521 41681 53381 57131 58199 63703 82939 84211 86137 86371 87691 106391 130439 136883 151013 157457 173867 174533 175631 221509 270059 271211 271549 406583 432457 440399 488441 576551 611999 675977 684127 696343 750151 822971 1010623 1168183 1304983 1629469 1790743 2327417 3464473 4187251 4834891 5240707 7080247 7313983 Last fiddled with by GP2 on 20180716 at 14:15 
20180716, 14:30  #424  
Sep 2003
5·11·47 Posts 
Quote:


20180716, 14:51  #425 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7·23·61 Posts 
PRPtop has a subset of these, too: http://www.primenumbers.net/prptop/s...&action=Search
(this search result requires additional filtering before use) 
20180716, 15:28  #426  
Sep 2003
5·11·47 Posts 
Quote:
It does include a handful of Mersenne numbers with nonprime exponents, but those all seem to be old discoveries from more than a decade ago. 

20180716, 18:52  #427 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7×23×61 Posts 
Yes, indeed  there is a selfinflicted 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 crossreference all sites every once in a while. 
20181012, 15:01  #428 
Sep 2003
A19_{16} Posts 
The 325th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M51487.
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. 
20181012, 15:43  #429  
Sep 2002
Database er0rr
2×29×71 Posts 
Quote:
Code:
time ./pfgw64 k f0 od q"(2^514871)/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 

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