23716957113345 · 2666666 - 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:23716957113345 · 2666666 - 1
Verification status (*):Proven
Official Comment:Arithmetic progression (3,d=2697434638065*2^666668)
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:200700   (log10 is 200699.83814829)
Rank (*):17574 (digit rank is 425)
Entrance Rank (*):2982
Currently on list? (*):short
Submitted:2/28/2011 12:42:33 CDT
Last modified:2/28/2011 13:20:21 CDT
Database id:98956
Status Flags:none
Score (*):41.699 (normalized score 0.1701)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 3, weight 48.7750997991033
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 213146, tag last modified 2012-02-13 15:51:05)

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_id98956
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 23716957113345 2 666666 -1 2>&1
[Elapsed time: 9.675 seconds]
modified2011-12-27 16:48:34
created2011-02-28 12:48:01
id127302

fieldvalue
prime_id98956
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/llr.pl 23716957113345*2^666666-1 2>&1
Starting Lucas Lehmer Riesel prime test of 23716957113345*2^666666-1
Using Zero Padded IBDWT : Mersenne fftlen = 32768, Used fftlen = 81920
V1 = 15 ; Computing U0...
V1 = 15 ; Computing U0...done.Starting Lucas-Lehmer loop...


23716957113345*2^666666-1 is prime! Time : 914.776 sec.
[Elapsed time: 15.95 minutes]
modified2011-03-25 10:27:29
created2011-02-28 12:52:40
id127303

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.