3124777373 · 7001# + 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:3124777373 · 7001# + 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (7,d=481789017*7001#)
Proof-code(s): (*):p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:3019   (log10 is 3018.8406449106)
Rank (*):96070 (digit rank is 2)
Entrance Rank (*):68886
Currently on list? (*):short
Submitted:2/9/2012 11:06:34 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:104454
Status Flags:none
Score (*):28.72 (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 2, weight 50.65381347788
Subcategory: "Arithmetic progression (7,d=*)"
(archival tag id 214033, 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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"3124777373*7001#+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 3124777373*7001#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.38% 3124777373*7001#+1 is prime! (3.4492s+0.0006s) [Elapsed time: 4.00 seconds]
modified2020-07-07 22:30:29
created2012-02-09 11:08:24

machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 3124777373 7001 # 1 2>&1 [Elapsed time: 365.331 seconds]
modified2020-07-07 22:30:28
created2012-02-09 17:10:21

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