U(2878, 1, 4620) - U(2878, 1, 4619)
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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(2878, 1, 4620) - U(2878, 1, 4619)
Verification status (*):PRP
Official Comment:Lehmer number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:15978   (log10 is 15977.539964103)
Rank (*):69081 (digit rank is 2)
Entrance Rank (*):56017
Currently on list? (*):no
Submitted:1/9/2013 11:22:54 CDT
Last modified:1/9/2013 11:50:40 CDT
Database id:110674
Status Flags:Verify
Score (*):33.8915 (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.
Lehmer number (archivable *)
Prime on list: no, rank 22
Subcategory: "Lehmer number"
(archival tag id 214903, tag last modified 2019-08-03 12:50:11)

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 15978 digits and 26.39% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/b9239.zip and a certificate compressed to 26MB in http://physics.open.ac.uk/~dbroadhu/cert/b9239_cert.gp.gz

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(2878,1,4620)-lucasU(2878,1,4619)" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing lucasU(2878,1,4620)-lucasU(2878,1,4619) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N-1 test using base 19
Running N-1 test using base 23
Running N+1 test using discriminant 31, base 10+sqrt(31)
Calling N-1 BLS with factored part 1.51% and helper 0.60% (5.14% proof)
lucasU(2878,1,4620)-lucasU(2878,1,4619) is Fermat and Lucas PRP! (153.9474s+0.0092s)
[Elapsed time: 2.57 minutes]
modified2013-02-02 20:51:49
created2013-01-09 11:27:49

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"lucasU(2878,1,4620)-lucasU(2878,1,4619)" 2>&1
PFGW Version [GWNUM 26.5]
lucasU(2878,1,46....asU(2878,1,4619) 1/1 mro=0

trial factoring to 4765056
lucasU(2878,1,4620)-lucasU(2878,1,4619) has no small factor.
[Elapsed time: 6.750 seconds]
modified2013-02-02 20:51:49
created2013-01-09 11:35:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.