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:

Verification status (*):PRP
Official Comment (*):Lucas primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E1 : Batalov, CM
Decimal Digits:17335   (log10 is 17334.270832907)
Rank (*):73571 (digit rank is 1)
Entrance Rank (*):71752
Currently on list? (*):short
Submitted:5/20/2022 17:56:04 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:133952
Status Flags:Verify, TrialDiv
Score (*):34.1437 (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.
Lucas primitive part (archivable *)
Prime on list: yes, rank 7
Subcategory: "Lucas primitive part"
(archival tag id 227057, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 102
Subcategory: "ECPP"
(archival tag id 227058, tag last modified 2023-03-11 16:02:30)

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: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
notesPFGW Version [GWNUM 29.8] Primality testing 1865661748...2962964481 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 59 Running N+1 test using discriminant 73, base 22+sqrt(73) Calling N-1 BLS with factored part 0.78% and helper 0.09% (2.44% proof) 1865661748...2962964481 is Fermat and Lucas PRP! (9.5281s+0.0012s) [Elapsed time: 9.00 seconds]
modified2022-07-11 18:21:44
created2022-05-20 18:01:02

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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