21000136731 · 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:21000136731 · 2333333 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L392 : Rodenkirk, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.55376678)
Rank (*):42347 (digit rank is 1403)
Entrance Rank (*):3893
Currently on list? (*):no
Submitted:9/15/2007 21:11:27 CDT
Last modified:9/15/2007 21:43:56 CDT
Removed (*):12/31/2007 10:09:48 CDT
Database id:82243
Status Flags:none
Score (*):39.5651 (normalized score 0.0112)

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 21000136731 2 333333 -1 2>&1
[Elapsed time: 9.383 seconds]
modified2011-12-27 16:48:49
created2007-09-15 21:22:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 21000136731*2^333333-1 2>&1
Starting Lucas Lehmer Riesel prime test of 21000136731*2^333333-1
V1 = 9 ; Computing U0...
Done Computing U0.
Starting Lucas-Lehmer loop...
21000136731*2^333333-1 is prime! Time: 1255.092 sec.
[Elapsed time: 20.92 minutes]
modified2007-10-11 15:01:44
created2007-09-15 21:23:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.