- E(6658)/85079

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: - E(6658)/85079
Verification status (*):PRP
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:21257   (log10 is 21256.010012513)
Rank (*):73188 (digit rank is 1)
Entrance Rank (*):66650
Currently on list? (*):short
Submitted:12/27/2020 03:28:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:131505
Status Flags:Verify
Score (*):34.7746 (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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 6
Subcategory: "Euler Irregular primes"
(archival tag id 225770, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 85
Subcategory: "ECPP"
(archival tag id 225771, tag last modified 2024-04-24 05:37:25)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (27 Dec 2020):  (report abuse)
Shown to be PRP by David Broadhurst in 2006.

Certificate at FactorDB.

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
notesPFGW Version [GWNUM 29.8] Primality testing 1023322475...3721298279 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.09% and helper 0.03% (0.31% proof) 1023322475...3721298279 is Fermat and Lucas PRP! (35.2613s+0.0026s) [Elapsed time: 36.00 seconds]
modified2021-04-20 22:39:25
created2020-12-27 03:31:15

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