U(2325, - 1, 7561)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:U(2325, - 1, 7561)
Verification status (*):PRP
Official Comment:Generalized Lucas number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x20 : Irvine, Water, Broadhurst
Decimal Digits:25451   (log10 is 25450.158163927)
Rank (*):63817 (digit rank is 1)
Entrance Rank (*):54018
Currently on list? (*):short
Submitted:10/4/2013 15:37:18 CDT
Last modified:10/4/2013 15:50:30 CDT
Database id:115822
Status Flags:Verify, TrialDiv
Score (*):35.3314 (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 217259, tag last modified 2019-10-03 13:50:20)

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.

David Broadhurst writes (11 Sep 2014): 
CHG proof at 25451 digits and 26.60% factorization with details here and a certificate compressed to 29 MB.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"lucasU(2325,-1,7561)" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing lucasU(2325,-1,7561) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N-1 BLS with factored part 0.95% and helper 0.22% (3.07% proof)
lucasU(2325,-1,7561) is Fermat and Lucas PRP! (237.9567s+0.0042s)
[Elapsed time: 3.97 minutes]
modified2013-10-21 18:10:45
created2013-10-04 15:38:01

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