69318339141 · 2371# + 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:69318339141 · 2371# + 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (9,d=1298717501*2371#)
Proof-code(s): (*):p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW
Decimal Digits:1014   (log10 is 1013.5910308424)
Rank (*):129174 (digit rank is 1923)
Entrance Rank (*):93457
Currently on list? (*):short
Submitted:8/1/2011 01:09:49 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:100962
Status Flags:none
Score (*):25.3142 (normalized score 0)

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 5, weight 51.343569876828
Subcategory: "Arithmetic progression (9,d=*)"
(archival tag id 213339, tag last modified 2023-03-11 15:53:59)

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_id100962
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 69318339141 2371 # 1 2>&1 [Elapsed time: 143.032 seconds]
modified2020-07-07 22:30:31
created2011-08-01 01:18:01
id131474

fieldvalue
prime_id100962
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"69318339141*2371#+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 69318339141*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.59% 69318339141*2371#+1 is prime! (0.3241s+0.0003s) [Elapsed time: 0.00 seconds]
modified2020-07-07 22:30:31
created2011-08-01 01:23:02
id131493

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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