31737014565 · 2140003 - 1
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The hardware and software on this system was updated September 4th.  Please let me know of any problem you encounter. <caldwell@utm.edu>

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:31737014565 · 2140003 - 1
Verification status (*):Proven
Official Comment:Sophie Germain (p)
Proof-code(s): (*):L95 : Urushi, LLR
Decimal Digits:42156   (log10 is 42155.604049015)
Rank (*):48882 (digit rank is 2)
Entrance Rank (*):31417
Currently on list? (*):short
Submitted:12/26/2010 06:17:47 CDT
Last modified:12/26/2010 06:50:23 CDT
Database id:97119
Status Flags:none
Score (*):36.8903 (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 8
Subcategory: "Sophie Germain (p)"
(archival tag id 213032, tag last modified 2012-04-11 10:50:29)

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.
fieldvalue
prime_id97119
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 31737014565 2 140003 -1 2>&1
[Elapsed time: 9.129 seconds]
modified2011-12-27 16:48:35
created2010-12-26 06:18:10
id123617

fieldvalue
prime_id97119
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/llr.pl 31737014565*2^140003-1 2>&1
Starting Lucas Lehmer Riesel prime test of 31737014565*2^140003-1
Using Zero Padded IBDWT : Mersenne fftlen = 7168, Used fftlen = 14336
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop...


31737014565*2^140003-1 is prime! Time : 29.335 sec.
[Elapsed time: 30.00 seconds]
modified2011-01-18 10:15:30
created2010-12-26 06:22:04
id123630

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.