379185609 · 227127 - 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:379185609 · 227127 - 1
Verification status (*):Proven
Official Comment:Cunningham chain (p)
Proof-code(s): (*):L983 : Wu_T, LLR
Decimal Digits:8175   (log10 is 8174.6195442233)
Rank (*):76106 (digit rank is 3)
Entrance Rank (*):46051
Currently on list? (*):no
Submitted:11/16/2009 15:20:49 CDT
Last modified:11/16/2009 15:50:23 CDT
Database id:90886
Status Flags:none
Score (*):31.8152 (normalized score 0)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Cunningham Chains (1st kind) (archivable class *)
Prime on list: no, rank 7, weight 21.9723862505027
Subcategory: "Cunningham chain (p)"
(archival tag id 212437, tag last modified 2016-11-20 06:50:35)

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 379185609 2 27127 -1 2>&1
[Elapsed time: 8.456 seconds]
modified2011-12-27 16:48:41
created2009-11-16 15:35:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/llr.pl 379185609*2^27127-1 2>&1
Starting Lucas Lehmer Riesel prime test of 379185609*2^27127-1
Using Zero Padded IBDWT : Mersenne fftlen = 1280, Used fftlen = 2560
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.
Starting Lucas-Lehmer loop...

379185609*2^27127-1 is prime! Time : 1.690 sec.
[Elapsed time: 2.00 seconds]
modified2009-11-24 13:57:49
created2009-11-16 15:33:11

Query times: 0.0013 seconds to select prime, 0.0008 seconds to seek comments.