607095 · 2176311 - 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:607095 · 2176311 - 1
Verification status (*):Proven
Official Comment:Sophie Germain (p)
Proof-code(s): (*):L983 : Wu_T, LLR
Decimal Digits:53081   (log10 is 53080.682822168)
Rank (*):52991 (digit rank is 2)
Entrance Rank (*):21143
Currently on list? (*):short
Submitted:9/18/2009 08:19:37 CDT
Last modified:9/18/2009 08:50:21 CDT
Database id:89999
Status Flags:none
Score (*):37.6015 (normalized score 0.0014)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 7
Subcategory: "Sophie Germain (p)"
(archival tag id 210514, tag last modified 2016-04-02 09:20:06)

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 607095 2 176311 -1 2>&1
[Elapsed time: 9.499 seconds]
modified2011-12-27 16:48:42
created2009-09-18 08:35:19

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 607095*2^176311-1 2>&1
Starting Lucas Lehmer Riesel prime test of 607095*2^176311-1
Using Irrational Base DWT : Mersenne fftlen = 10240, Used fftlen = 16384
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.
Starting Lucas-Lehmer loop...

607095*2^176311-1 is prime! Time : 72.255 sec.
[Elapsed time: 72.00 seconds]
modified2009-11-24 13:57:51
created2009-09-18 08:31:12

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.