68002763264 · 2749# - 1
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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:68002763264 · 2749# - 1
Verification status (*):Proven
Official Comment:Cunningham chain (16p+15)
Proof-code(s): (*):p35 : Augustin, NewPGen, OpenPFGW
Decimal Digits:1185   (log10 is 1184.0621976254)
Rank (*):110759 (digit rank is 56)
Entrance Rank (*):89086
Currently on list? (*):short
Submitted:3/4/2012 14:50:52 CDT
Last modified:3/6/2012 12:50:06 CDT
Database id:105346
Status Flags:none
Score (*):25.8004 (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.
Cunningham Chains (1st kind) (archivable class *)
Prime on list: yes, rank 4, weight 46.5238297245122
Subcategory: "Cunningham chain (16p+15)"
(archival tag id 214228, tag last modified 2016-10-15 14:50:51)

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 -tp -q"68002763264*2749#-1" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 68002763264*2749#-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 2753, base 1+sqrt(2753)
Calling Brillhart-Lehmer-Selfridge with factored part 33.54%
68002763264*2749#-1 is prime! (2.1562s+0.0005s)
[Elapsed time: 2.00 seconds]
modified2012-07-16 11:33:02
created2012-03-04 14:53:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 68002763264 2749 # -1 2>&1
[Elapsed time: 163.071 seconds]
modified2012-03-04 14:54:45
created2012-03-04 14:52:02

Query times: 0.0002 seconds to select prime, 0.0001 seconds to seek comments.