3911 · 2462579 + 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:3911 · 2462579 + 1
Verification status (*):Proven
Official Comment:Divides GF(462577,10)
Proof-code(s): (*):L679 : Foody, Srsieve, PrimeGrid, LLR
Decimal Digits:139254   (log10 is 139253.74665206)
Rank (*):35841 (digit rank is 2)
Entrance Rank (*):3860
Currently on list? (*):no
Submitted:7/19/2009 10:26:33 CDT
Last modified:7/19/2009 11:20:22 CDT
Database id:89334
Status Flags:none
Score (*):40.5741 (normalized score 0.0298)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 23, weight 48.8456798530849
Subcategory: "Divides GF(*,10)"
(archival tag id 210477, tag last modified 2017-08-24 21:20:02)

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.
fieldvalue
prime_id89334
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 3911 2 462579 1 2>&1
[Elapsed time: 9.519 seconds]
modified2011-12-27 16:48:43
created2009-07-19 10:35:11
id108037

fieldvalue
prime_id89334
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"3911*2^462579+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 3911*2^462579+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(57344,20) to FFT(57344,19)
Reduced from FFT(57344,19) to FFT(57344,18)
Reduced from FFT(57344,18) to FFT(57344,17)
925190 bit request FFT size=(57344,17)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
3911*2^462579+1 is prime! (1267.2900s+0.0000s)
[Elapsed time: 21.95 minutes]
modified2009-08-11 11:44:23
created2009-07-19 10:53:01
id108039

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