39 · 22705367 + 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:39 · 22705367 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(2705360,3)
Proof-code(s): (*):L1576 : Craig, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:814399   (log10 is 814398.20734408)
Rank (*):3750 (digit rank is 1)
Entrance Rank (*):99
Currently on list? (*):yes
Submitted:4/28/2013 22:06:54 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:113986
Status Flags:none
Score (*):46.003 (normalized score 2.3576)

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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 14, weight 49.666568675772
Subcategory: "Divides GF(*,3)"
(archival tag id 217107, tag last modified 2024-03-22 08:37:11)

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_id113986
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"39*2^2705367+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 39*2^2705367+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 39*2^2705367+1 is prime! (15340.7283s+0.0018s) [Elapsed time: 4.26 hours]
modified2020-07-07 22:30:19
created2013-04-28 22:08:02
id158331

fieldvalue
prime_id113986
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 39 2 2705367 1 2>&1 [Elapsed time: 11.050 seconds]
modified2020-07-07 22:30:19
created2013-04-28 22:18:02
id158332

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