51 · 26945567 + 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:51 · 26945567 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(6945564,12) [p286]
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:2090826   (log10 is 2090825.7114641)
Rank (*):201 (digit rank is 1)
Entrance Rank (*):81
Currently on list? (*):short
Submitted:5/27/2020 03:36:06 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:130928
Status Flags:none
Score (*):48.8948 (normalized score 60.8644)

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 6, weight 52.826661468463
Subcategory: "Divides GF(*,12)"
(archival tag id 224036, 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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/4/pfgw64 -t -q"51*2^6945567+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 51*2^6945567+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 51*2^6945567+1 is prime! (20145.1838s+0.0030s) [Elapsed time: 5.60 hours]
modified2020-07-07 22:30:10
created2020-05-27 03:41:02

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.
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