39 · 21824871 + 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 · 21824871 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(1824867,6)
Proof-code(s): (*):L2664 : Koluvere, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:549343   (log10 is 549342.50028193)
Rank (*):6607 (digit rank is 1)
Entrance Rank (*):127
Currently on list? (*):short
Submitted:9/6/2011 02:49:37 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:101820
Status Flags:none
Score (*):44.7941 (normalized score 0.8331)

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 19, weight 48.457749828214
Subcategory: "Divides GF(*,6)"
(archival tag id 213412, tag last modified 2023-03-31 01:37:05)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 39 2 1824871 1 2>&1 [Elapsed time: 10.494 seconds]
modified2020-07-07 22:30:31
created2011-09-06 02:52:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"39*2^1824871+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 39*2^1824871+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 39*2^1824871+1 is prime! (4781.1799s+0.0236s) [Elapsed time: 79.68 minutes]
modified2020-07-07 22:30:31
created2011-09-06 02:52:45

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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