31365193335 · 2666674 - 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:31365193335 · 2666674 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1735 : Williams2, TwinGen, PrimeGrid, LLR
Decimal Digits:200700   (log10 is 200699.36777726)
Rank (*):26633 (digit rank is 1971)
Entrance Rank (*):2177
Currently on list? (*):no
Submitted:9/21/2010 08:45:05 CDT
Last modified:9/21/2010 17:20:23 CDT
Removed (*):7/10/2011 19:10:17 CDT
Database id:95067
Status Flags:none
Score (*):41.699 (normalized score 0.0861)

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 31365193335 2 666674 -1 2>&1
[Elapsed time: 9.814 seconds]
modified2011-12-27 16:48:37
created2010-09-21 08:48:12

machineVista on Core 2 6700 2.66GHz
notesCommand: pfgw.exe -n -tp -q"31365193335*2^666674-1" 2>&1
Primality testing 31365193335*2^666674-1 [N+1, Brillhart-Lehmer-Selfridge]
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N+1 test using discriminant 11, base 1+sqrt(11)
N+1: 31Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
31365193335*2^666674-1 is prime! (15461.2946s+0.0594s)
365193335*2^666674-1[Elapsed time: 15461 seconds]
modified2011-12-27 16:48:37
created2010-09-21 12:35:43

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.