14962863771 · 2140001 - 1
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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:14962863771 · 2140001 - 1
Verification status (*):Proven
Official Comment:Sophie Germain (p)
Proof-code(s): (*):L95 : Urushi, LLR
Decimal Digits:42155   (log10 is 42154.675437675)
Rank (*):48741 (digit rank is 6)
Entrance Rank (*):31417
Currently on list? (*):short
Submitted:12/26/2010 06:17:46 CDT
Last modified:12/26/2010 06:20:28 CDT
Database id:97113
Status Flags:none
Score (*):36.8902 (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 9
Subcategory: "Sophie Germain (p)"
(archival tag id 213030, 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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 14962863771 2 140001 -1 2>&1
[Elapsed time: 8.769 seconds]
modified2011-12-27 16:48:35
created2010-12-26 06:19:05

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/llr.pl 14962863771*2^140001-1 2>&1
Starting Lucas Lehmer Riesel prime test of 14962863771*2^140001-1
Using Zero Padded IBDWT : Mersenne fftlen = 7168, Used fftlen = 14336
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop...

14962863771*2^140001-1 is prime! Time : 29.334 sec.
[Elapsed time: 30.00 seconds]
modified2011-01-18 10:15:30
created2010-12-26 06:19:06

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