125848198864 · 4253# + 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:125848198864 · 4253# + 1
Verification status (*):Proven
Official Comment:Cunningham chain 2nd kind (8p-7)
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:1829   (log10 is 1828.98317206)
Rank (*):96028 (digit rank is 1)
Entrance Rank (*):69657
Currently on list? (*):short
Submitted:11/14/2010 05:50:22 CDT
Last modified:11/14/2010 06:20:23 CDT
Database id:96193
Status Flags:none
Score (*):27.1583 (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 (2nd kind) (archivable class *)
Prime on list: yes, rank 5, weight 42.1383923691983
Subcategory: "Cunningham chain 2nd kind (8p-7)"
(archival tag id 212984, tag last modified 2018-05-09 09:50:23)

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/TrialDiv/TrialDiv -q 125848198864 4253 # 1 2>&1
[Elapsed time: 236.787 seconds]
modified2011-12-27 16:48:36
created2010-11-14 05:52:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"125848198864*4253#+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 125848198864*4253#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 4259
Calling Brillhart-Lehmer-Selfridge with factored part 33.35%
125848198864*4253#+1 is prime! (1.5000s+0.0000s)
[Elapsed time: 2.00 seconds]
modified2010-11-28 11:14:55
created2010-11-14 05:53:01

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.