5 · 2125413 + 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:5 · 2125413 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(125410); GF(125410,5), GF(125408,10) [g0]; GF(125410,5) [p50]
Proof-code(s): (*):Y : Young
Decimal Digits:37754   (log10 is 37753.7738162112)
Rank (*):57755 (digit rank is 1)
Entrance Rank (*):6
Currently on list? (*):no
Submitted:8/1995
Last modified:8/1995
Database id:2598
Status Flags:none
Score (*):36.5498 (normalized score 0.0005)

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 38, weight 38.1592883758678
Subcategory: "Divides GF(*,10)"
(archival tag id 190721, tag last modified 2017-08-24 21:20:02)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 44, weight 38.1592883758678
Subcategory: "Divides GF(*,5)"
(archival tag id 190720, tag last modified 2019-10-16 18:20:19)
Fermat Divisors (archivable *)
Prime on list: no, rank 35, weight 38.1592883758678
Subcategory: "Divides Fermat"
(archival tag id 190719, tag last modified 2016-03-15 13:57:14)

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_id2598
person_id9
machineAthlon 1.3GHz WinXP
whatprime
notesProth.exe 7.1 (verification : a = 3)
modified2003-03-25 11:23:59
created2002-12-25 08:40:42
id51797

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.