492590931 · 280000 - 1631979959 · 225001 - 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:492590931 · 280000 - 1631979959 · 225001 - 1
Verification status (*):PRP
Official Comment:Arithmetic progression (4,d=164196977*2^80000-1631979959*2^25000)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:24092   (log10 is 24091.09213953)
Rank (*):63591 (digit rank is 4)
Entrance Rank (*):38518
Currently on list? (*):short
Submitted:10/24/2010 16:44:10 CDT
Last modified:10/24/2010 17:20:22 CDT
Database id:95651
Status Flags:Verify
Score (*):35.1618 (normalized score 0.0001)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 1, weight 46.4562230293586
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 210865, tag last modified 2016-03-15 13:57:14)

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): 
KP proof

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"492590931*2^80000-1631979959*2^25001-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 7414792
492590931*2^80000-1631979959*2^25001-1 has no small factor.
[Elapsed time: 14.354 seconds]
modified2011-12-27 16:48:36
created2010-10-24 16:48:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -tp -q"492590931*2^80000-1631979959*2^25001-1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 492590931*2^80000-1631979959*2^25001-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 31.24%
492590931*2^80000-1631979959*2^25001-1 is Lucas PRP! (117.5067s+0.0005s)
[Elapsed time: 2.12 minutes]
modified2010-11-28 11:14:56
created2010-10-24 16:48:40

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.