2316765173284 · 3593# + 16067

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:2316765173284 · 3593# + 16067
Verification status (*):PRP
Official Comment (*):Quintuplet (3), ECPP
Proof-code(s): (*):c18 : Luhn, Primo
Decimal Digits:1543   (log10 is 1542.7749052196)
Rank (*):109399 (digit rank is 3)
Entrance Rank (*):93763
Currently on list? (*):short
Submitted:10/15/2016 19:33:14 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:122378
Status Flags:Verify
Score (*):26.6272 (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 1006
Subcategory: "ECPP"
(archival tag id 218465, tag last modified 2024-07-11 00:37:12)
Quintuplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Quintuplet (3)"
(archival tag id 218466, tag last modified 2023-03-11 15:53:59)

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"2316765173284*3593#+16067" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 2316765173284*3593#+16067 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.64% and helper 0.25% (2.24% proof) 2316765173284*3593#+16067 is Fermat and Lucas PRP! (0.4336s+0.0006s) [Elapsed time: 0.00 seconds]
modified2020-07-07 22:30:16
created2016-10-15 19:42:52

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