31 · 2421129 - 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help)value
Description:31 · 2421129 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L637 : DeTroia, NewPGen, PRP, OpenPFGW, LLR
Decimal Digits:126774   (log10 is 126773.95240567)
Rank (*):37127 (digit rank is 1)
Entrance Rank (*):2802
Currently on list? (*):no
Submitted:12/9/2008 08:31:56 CDT
Last modified:12/9/2008 08:50:27 CDT
Removed (*):6/21/2009 07:31:28 CDT
Database id:85894
Status Flags:none
Score (*):40.285 (normalized score 0.0234)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 31 2 421129 -1 2>&1
[Elapsed time: 9.650 seconds]
modified2011-12-27 16:48:46
created2008-12-09 08:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 31*2^421129-1 2>&1
Starting Lucas Lehmer Riesel prime test of 31*2^421129-1
Using Irrational Base DWT : Mersenne fftlen = 20480, Used fftlen = 24576
V1 = 4 ; Computing U0...
V1 = 4 ; Computing U0...done.
Starting Lucas-Lehmer loop...

31*2^421129-1 is prime! Time : 265.738 sec.
[Elapsed time: 4.43 minutes]
modified2009-02-05 12:51:35
created2008-12-09 08:38:02

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.