20170207, 01:34  #1 
Aug 2015
2·23 Posts 
Fully factored
Is there a "fully TF'd" list of exponents on mersenne.ca?

20170207, 04:54  #2 
"Curtis"
Feb 2005
Riverside, CA
2·3·7·113 Posts 
Define "fully TF'ed". Do you mean fully factored?

20170207, 18:57  #3 
Aug 2015
56_{8} Posts 
Yes, fully factored

20170207, 19:21  #4 
Mar 2014
48_{10} Posts 
This would be an interesting list to see.
I suspect there are very few large exponents on the list  finding one 60 or 70bit factor of a milliondigit number leaves a very large nut to crack. 
20170207, 20:44  #5 
"Curtis"
Feb 2005
Riverside, CA
2·3·7·113 Posts 
Check the top5000 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? 
20170207, 21:25  #7 
Sep 2002
Database er0rr
2·7^{2}·37 Posts 
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 Here the reported gigantic PRPs  I dare say Henri's list is out of date, in that some PRPs are proven primes.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. 
20170208, 04:02  #8  
Sep 2003
2^{2}·647 Posts 
Quote:
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). 

20170208, 04:08  #9 
Sep 2003
2^{2}×647 Posts 
Yes, here is the complete list. There are currently 310 fullyfactored or probablyfullyfactored 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 probableprime (PRP) cofactor, albeit with extremely high confidence. Last fiddled with by GP2 on 20170208 at 04:12 
20170208, 17:35  #10  
"Mike"
Aug 2002
1F7C_{16} Posts 
Quote:


20170208, 18:30  #11  
Sep 2003
2^{2}×647 Posts 
Quote:
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. Last fiddled with by GP2 on 20170208 at 18:32 

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