798 · Bern(8766)/14670751334144820770719

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:798 · Bern(8766)/14670751334144820770719
Verification status (*):PRP
Official Comment (*):Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c94 : Gelhar, Ritschel, TOPS, Primo
Decimal Digits:23743   (log10 is 23742.134574679)
Rank (*):72613 (digit rank is 2)
Entrance Rank (*):66099
Currently on list? (*):short
Submitted:1/4/2021 14:05:40 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:131539
Status Flags:Verify
Score (*):35.1167 (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.
Irregular Primes (archivable *)
Prime on list: yes, rank 3
Subcategory: "Irregular Primes"
(archival tag id 225782, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 64
Subcategory: "ECPP"
(archival tag id 225783, 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.

Robert Gelhar writes (4 Jan 2021):  (report abuse)
http://factordb.com/index.php?id=1100000002364864121 is the id for the certificate for this prime at FactorDB, which is currently in the process of double checking as of the writing of this comment.

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 4c+4c 3.5GHz
notesPFGW Version [GWNUM 29.8] Primality testing 1363247402...3245956061 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 13 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N+1 BLS with factored part 0.04% and helper 0.04% (0.17% proof) 1363247402...3245956061 is Fermat and Lucas PRP! (50.1297s+0.0031s) [Elapsed time: 50.00 seconds]
modified2021-04-20 22:39:25
created2021-01-04 14:06:14

Query times: 0.0003 seconds to select prime, 0.0009 seconds to seek comments.
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