21082112331 · 2333333 - 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.

This prime's information:

Description:21082112331 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L438 : Andersen2, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.55545878)
Rank (*):48046 (digit rank is 1395)
Entrance Rank (*):4142
Currently on list? (*):no
Submitted:10/13/2007 19:36:49 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):1/1/2008 16:04:40 UTC
Database id:82548
Status Flags:none
Score (*):39.5651 (normalized score 0.0054)

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/llr.pl 21082112331*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 21082112331*2^333333-1 V1 = 11 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 21082112331*2^333333-1 is prime! Time: 1290.865 sec. [Elapsed time: 21.52 minutes]
modified2020-07-07 22:30:40
created2007-10-13 19:39:13

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 21082112331 2 333333 -1 2>&1 [Elapsed time: 9.587 seconds]
modified2020-07-07 22:30:40
created2007-10-13 19:52:59

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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