31737014565 · 2140003 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

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 (*):58037 (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 0.0005)

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 16
Subcategory: "Sophie Germain (p)"
(archival tag id 213032, tag last modified 2020-05-17 15:50:28)

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 31737014565 2 140003 -1 2>&1 [Elapsed time: 9.129 seconds]
modified2020-07-07 17:30:32
created2010-12-26 06:18:10

machineRedHat Virtual STEM Server
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]
modified2020-07-07 17:30:32
created2010-12-26 06:22:04

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.