12656813631 · 2333333 - 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:12656813631 · 2333333 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L365 : Stoll, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.33386905)
Rank (*):43709 (digit rank is 2118)
Entrance Rank (*):3577
Currently on list? (*):no
Submitted:6/18/2007 22:45:25 CDT
Last modified:6/19/2007 00:30:12 CDT
Removed (*):10/23/2007 23:04:28 CDT
Database id:81147
Status Flags:none
Score (*):39.5651 (normalized score 0.0102)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 12656813631 2 333333 -1 2>&1
[Elapsed time: 9.262 seconds]
modified2007-09-12 06:50:19
created2007-06-18 22:52:11

machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 12656813631*2^333333-1 2>&1
Starting Lucas Lehmer Riesel prime test of 12656813631*2^333333-1
V1 = 11 ; Computing U0...
Done Computing U0.
Starting Lucas-Lehmer loop...
12656813631*2^333333-1 is prime! Time: 1248.990 sec.
[Elapsed time: 1249 seconds]
modified2007-09-12 06:50:19
created2007-06-19 00:09:23

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.