U(5768, - 5769, 4591)

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:U(5768, - 5769, 4591)
Verification status (*):PRP
Official Comment (*):Generalized Lucas number, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x45 : Batalov, OpenPFGW, Primo, Unknown
Decimal Digits:17264   (log10 is 17263.451398544)
Rank (*):74201 (digit rank is 1)
Entrance Rank (*):66967
Currently on list? (*):short
Submitted:11/8/2018 10:06:59 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:125770
Status Flags:Verify
Score (*):34.131 (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.
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 20
Subcategory: "Generalized Lucas Number"
(archival tag id 219965, tag last modified 2023-03-11 16:02:31)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 14
Subcategory: "Cyclotomy Proof"
(archival tag id 219966, tag last modified 2023-03-11 15:53:59)

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.

Serge Batalov writes (8 Nov 2018):  (report abuse)
K-P with N-1 factored 31.0% (helpers can be found in N-1, with the larger p4333 proven with Primo)

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"lucasU(5768,-5769,4591)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing lucasU(5768,-5769,4591) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 29 Running N-1 test using base 47 Running N-1 test using base 83 Running N+1 test using discriminant 101, base 4+sqrt(101) Calling N-1 BLS with factored part 0.92% and helper 0.02% (2.80% proof) lucasU(5768,-5769,4591) is Fermat and Lucas PRP! (37.0425s+0.0022s) [Elapsed time: 37.00 seconds]
modified2020-07-07 22:30:14
created2018-11-08 10:11:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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