U(1624, - 1, 10169)

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Description:U(1624, - 1, 10169)
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:32646   (log10 is 32645.240375426)
Rank (*):61780 (digit rank is 1)
Entrance Rank (*):58166
Currently on list? (*):short
Submitted:11/11/2018 23:37:48 CDT
Last modified:11/11/2018 23:50:21 CDT
Database id:125781
Status Flags:Verify, TrialDiv
Score (*):36.1008 (normalized score 0.0002)

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 6
Subcategory: "Generalized Lucas Number"
(archival tag id 219972, tag last modified 2020-05-28 13:20:28)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 5
Subcategory: "Cyclotomy Proof"
(archival tag id 219973, tag last modified 2019-06-27 21:50:21)

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 (12 Nov 2018):  (report abuse)
K-P with N-1 factored 30.77%, with the larger p7668 and p2142 proven with Primo.

N-1 cofactors:
primV(1624,-1,2542)/199516573522119490120154829286218330881
primV(1624,-1,1017)/31629088768433383

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.
fieldvalue
prime_id125781
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"lucasU(1624,-1,10169)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing lucasU(1624,-1,10169) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 23, base 6+sqrt(23) Calling N-1 BLS with factored part 0.29% and helper 0.18% (1.06% proof) lucasU(1624,-1,10169) is Fermat and Lucas PRP! (95.4408s+0.0026s) [Elapsed time: 1.58 minutes]
modified2020-07-07 17:30:14
created2018-11-11 23:41:02
id171458

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.
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