3 · 23136255 - 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:3 · 23136255 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L256 : Underwood, Srsieve, NewPGen, 321search, LLR
Decimal Digits:944108   (log10 is 944107.30617239)
Rank (*):713 (digit rank is 1)
Entrance Rank (*):12
Currently on list? (*):short
Submitted:3/8/2007 21:49:13 CDT
Last modified:3/9/2007 17:15:18 CDT
Database id:79671
Status Flags:none
Score (*):46.4565 (normalized score 10.1125)

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 3 2 3136255 -1 2>&1
[Elapsed time: 11.409 seconds]
modified2007-04-21 22:36:37
created2007-03-08 21:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 3*2^3136255-1 2>&1
Starting Lucas Lehmer Riesel prime test of 3*2^3136255-1
V1 = 3 ; Computing U0...
Done Computing U0.
Starting Lucas-Lehmer loop...
3*2^3136255-1 is prime! Time : 65367.129 sec.
[Elapsed time: 65368 seconds]
modified2007-04-21 22:36:37
created2007-03-08 23:05:50

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.