625 · 21410668 + 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:625 · 21410668 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1498 : Goral, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:424657   (log10 is 424656.17780333)
Rank (*):5435 (digit rank is 1)
Entrance Rank (*):342
Currently on list? (*):no
Submitted:1/27/2012 16:57:06 CDT
Last modified:1/27/2012 19:48:43 CDT
Removed (*):6/4/2019 21:11:41 CDT
Database id:104079
Status Flags:none
Score (*):44.0033 (normalized score 0.9341)

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 (archivable *)
Prime on list: no, rank 961
Subcategory: "Generalized Fermat"
(archival tag id 213808, tag last modified 2019-12-09 01:50:25)

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.

Jon Goral writes (11 Sep 2014): 
Divides xGF(1410667,5,3)

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_id104079
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 625 2 1410668 1 2>&1
[Elapsed time: 10.249 seconds]
modified2012-02-19 19:07:47
created2012-01-27 17:05:23
id137747

fieldvalue
prime_id104079
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"625*2^1410668+1" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing 625*2^1410668+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
625*2^1410668+1 is prime! (2426.2973s+0.0015s)
[Elapsed time: 40.60 minutes]
modified2012-02-19 19:07:47
created2012-01-27 17:41:04
id137749

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