U(13283, 1, 3697) + U(13283, 1, 3696)
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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(13283, 1, 3697) + U(13283, 1, 3696)
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:15240   (log10 is 15239.702677696)
Rank (*):68836 (digit rank is 1)
Entrance Rank (*):46982
Currently on list? (*):no
Submitted:4/25/2011 16:44:14 CDT
Last modified:4/25/2011 17:20:19 CDT
Database id:99848
Status Flags:Verify
Score (*):33.7451 (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 25
Subcategory: "Lehmer number"
(archival tag id 213223, 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 with an ECPP proof of a helper with 1945 digits

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"lucasU(13283,1,3697)+lucasU(13283,1,3696)" 2>&1
PFGW Version [GWNUM 26.5]
lucasU(13283,1,3....sU(13283,1,3696) 1/1 mro=0

trial factoring to 4528256
lucasU(13283,1,3697)+lucasU(13283,1,3696) has no small factor.
[Elapsed time: 7.146 seconds]
modified2011-12-27 16:48:33
created2011-04-25 16:48:24

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"lucasU(13283,1,3697)+lucasU(13283,1,3696)" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing lucasU(13283,1,3697)+lucasU(13283,1,3696) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N-1 test using base 53
Running N+1 test using discriminant 73, base 4+sqrt(73)
Calling N-1 BLS with factored part 1.44% and helper 0.26% (4.57% proof)
lucasU(13283,1,3697)+lucasU(13283,1,3696) is Fermat and Lucas PRP! (123.3996s+0.0041s)
[Elapsed time: 2.05 minutes]
modified2011-05-17 08:18:57
created2011-04-25 16:48:47

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.