Phi(3, 10103182) + (137 · 10103183 + 731 · 1066639) · (1036543 - 1)/999
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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:Phi(3, 10103182) + (137 · 10103183 + 731 · 1066639) · (1036543 - 1)/999
Verification status (*):PRP
Official Comment:Palindrome
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x29 : Broadhurst, OpenPFGW
Decimal Digits:206365   (log10 is 206364)
Rank (*):23199 (digit rank is 1)
Entrance Rank (*):14815
Currently on list? (*):short
Submitted:1/31/2014 08:49:30 CDT
Last modified:1/31/2014 16:20:55 CDT
Database id:117033
Status Flags:Verify, TrialDiv
Score (*):41.7847 (normalized score 0.1036)

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.
Palindrome (archivable *)
Prime on list: yes, rank 20
Subcategory: "Palindrome"
(archival tag id 217596, tag last modified 2016-01-10 02:20:35)

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): 
1 (0)_{66638} (137)_{12181} 1 (731)_{12181} (0)_{66638} 1 with KP proof at 32.29% factorization

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 -tc -q"Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^36543-1)/999" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^36543-1)/999 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 32.29% and helper 0.00% (96.88% proof)
Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^36543-1)/999 is Fermat and Lucas PRP! (25257.7512s+0.1102s)
[Elapsed time: 7.02 hours]
modified2014-04-01 17:37:38
created2014-01-31 08:53:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.