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 cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E1 : Batalov, CM
Decimal Digits:20911   (log10 is 20910.05875532)
Rank (*):73303 (digit rank is 1)
Entrance Rank (*):72919
Currently on list? (*):short
Submitted:4/2/2024 22:37:05 UTC
Last modified:4/2/2024 23:37:13 UTC
Database id:137917
Status Flags:Verify
Score (*):34.7239 (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 90
Subcategory: "ECPP"
(archival tag id 229474, tag last modified 2024-04-24 05:37:25)
Lucas cofactor (archivable *)
Prime on list: yes, rank 5
Subcategory: "Lucas cofactor"
(archival tag id 229475, tag last modified 2024-04-24 05:37:27)

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: Digital Ocean Droplet
notesPFGW Version [GWNUM 30.11]
Primality testing V(100417)/7130429037...5470448849 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 69462-bit number
Running N+1 test using discriminant 17, base 6+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 69462-bit number
Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.23% proof)

V(100417)/7130429037...5470448849 is Fermat and Lucas PRP! (19.0697s+0.0084s)
[Elapsed time: 20.00 seconds]
modified2024-04-02 22:38:41
created2024-04-02 22:38:21

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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