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.

Verification status (*):PRP
Official Comment (*):Lucas cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:18049   (log10 is 18048.606251286)
Rank (*):70332 (digit rank is 2)
Entrance Rank (*):68885
Currently on list? (*):short
Submitted:9/11/2020 11:57:38 CDT
Last modified:9/11/2020 12:20:21 CDT
Database id:131232
Status Flags:Verify, TrialDiv
Score (*):34.2687 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 51
Subcategory: "ECPP"
(archival tag id 225659, tag last modified 2021-09-18 09:37:41)
Lucas cofactor (archivable *)
Prime on list: yes, rank 1
Subcategory: "Lucas cofactor"
(archival tag id 225660, tag last modified 2020-09-11 12:20:26)

User comments about this prime (disclaimer):

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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
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(86477)/1042112515940998434071039" 2>&1 PFGW Version [GWNUM 29.8] Primality testing V(86477)/1042112515...8434071039 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.16% proof) V(86477)/1042112515...8434071039 is Fermat and Lucas PRP! (24.1791s+0.0063s) [Elapsed time: 24.00 seconds]
modified2021-04-20 17:39:26
created2020-09-11 12:01:02

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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