U(1404, - 1, 9209)

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.

Description:U(1404, - 1, 9209)
Verification status (*):PRP
Official Comment (*):Generalized Lucas number, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH10 : Batalov, OpenPFGW, Primo, CHG
Decimal Digits:28981   (log10 is 28980.958357032)
Rank (*):65061 (digit rank is 2)
Entrance Rank (*):61445
Currently on list? (*):short
Submitted:11/12/2018 02:33:44 CDT
Last modified:11/12/2018 02:50:15 CDT
Database id:125782
Status Flags:Verify, TrialDiv
Score (*):35.7329 (normalized score 0.0001)

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 8
Subcategory: "Generalized Lucas Number"
(archival tag id 219974, tag last modified 2020-05-28 13:20:28)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 6
Subcategory: "Cyclotomy Proof"
(archival tag id 219975, 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)
CHG proof with N+1 factored 14.03% and N-1, 13.18%, with the p3839 and p3598 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(1404,-1,9209)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing lucasU(1404,-1,9209) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 31, base 12+sqrt(31) Calling N-1 BLS with factored part 0.23% and helper 0.12% (0.81% proof) lucasU(1404,-1,9209) is Fermat and Lucas PRP! (62.4758s+0.0009s) [Elapsed time: 63.00 seconds]
modified2020-07-07 17:30:14
created2018-11-12 02:41:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.