U(2449, - 1, 12671)

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(2449, - 1, 12671)
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:42939   (log10 is 42938.48882491)
Rank (*):58411 (digit rank is 1)
Entrance Rank (*):54827
Currently on list? (*):short
Submitted:11/21/2018 18:31:58 CDT
Last modified:11/21/2018 18:50:17 CDT
Database id:125807
Status Flags:Verify, TrialDiv
Score (*):36.9471 (normalized score 0.0005)

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 3
Subcategory: "Generalized Lucas Number"
(archival tag id 219987, tag last modified 2020-05-28 13:20:28)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 1
Subcategory: "Cyclotomy Proof"
(archival tag id 219988, tag last modified 2018-11-21 18:50:17)

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 (21 Nov 2018):  (report abuse)
BLS with N+1 factored part 30.76% and helper 7.85% with p12998 and p1620 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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"lucasU(2449,-1,12671)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing lucasU(2449,-1,12671) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 59 Running N-1 test using base 83 Running N-1 test using base 107 Running N+1 test using discriminant 113, base 2+sqrt(113) Calling N-1 BLS with factored part 0.64% and helper 0.17% (2.09% proof) lucasU(2449,-1,12671) is Fermat and Lucas PRP! (232.4249s+0.0037s) [Elapsed time: 3.88 minutes]
modified2020-07-07 17:30:14
created2018-11-21 18:33:01

Query times: 0.0005 seconds to select prime, 0.0011 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.