primV(12215, - 1, 13500)
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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:primV(12215, - 1, 13500)
Verification status (*):PRP
Official Comment:Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:29426   (log10 is 29425.633014385)
Rank (*):62410 (digit rank is 1)
Entrance Rank (*):58495
Currently on list? (*):short
Submitted:7/21/2016 20:49:08 CDT
Last modified:7/21/2016 21:20:26 CDT
Database id:121930
Status Flags:Verify, TrialDiv
Score (*):35.78 (normalized score 0.0002)

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 primitive part (archivable *)
Prime on list: yes, rank 12
Subcategory: "Generalized Lucas primitive part"
(archival tag id 218368, tag last modified 2016-07-21 21:20:29)

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 (21 Jul 2016): 
CHG proof at 29426 digits and 26.78% factorization with details in and a certificate compressed to 6 MB in

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 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"primV(12215,-1,13500)" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing primV(12215,-1,13500) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 53
Running N-1 test using base 67
Running N-1 test using base 83
Running N+1 test using discriminant 107, base 1+sqrt(107)
Calling N-1 BLS with factored part 1.57% and helper 0.03% (4.74% proof)

primV(12215,-1,13500) is Fermat and Lucas PRP! (95.2617s+0.0375s)
[Elapsed time: 1.58 minutes]
modified2017-01-27 05:57:11
created2016-07-21 20:51:01

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