137211941292195 · 2171960 - 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:137211941292195 · 2171960 - 1
Verification status (*):Proven
Official Comment:Sophie Germain (p)
Proof-code(s): (*):x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown
Decimal Digits:51780   (log10 is 51779.2554462871)
Rank (*):53595 (digit rank is 4)
Entrance Rank (*):10171
Currently on list? (*):short
Submitted:5/3/2006 05:22:30 CDT
Last modified:7/7/2006 10:39:03 CDT
Database id:77705
Status Flags:none
Score (*):37.5249 (normalized score 0.0013)

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 9
Subcategory: "Sophie Germain (p)"
(archival tag id 189940, 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.
machineWinXP P4 2.2GHz By K
notesCommand: pfgw.exe -n -f -tp -q"137211941292195*2^171960-1" 2>&1
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 137211941292195*2^171960-1 [N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 16858041
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
137211941292195*2^171960-1 is prime! (1718.6315s+0.0037s)
[Elapsed time: 1719 seconds]
modified2006-07-14 06:27:05
created2006-05-04 00:03:39

machineGenToo P3 400MHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 137211941292195 2 171960 -1 2>&1
[Elapsed time: 9.457 seconds]
modified2006-07-14 06:27:03
created2006-07-07 10:38:54

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.