E(660)/(19825 · 3318810147166091 · 13270662249997061963929586463495619)
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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:E(660)/(19825 · 3318810147166091 · 13270662249997061963929586463495619)
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c63 : Ritschel, TOPS, Primo
Decimal Digits:1393   (log10 is 1392.7982592159)
Rank (*):99521 (digit rank is 5)
Entrance Rank (*):95840
Currently on list? (*):short
Submitted:2/6/2017 04:56:30 CDT
Last modified:2/6/2017 05:20:39 CDT
Database id:122869
Status Flags:Verify, TrialDiv
Score (*):26.3078 (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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 19
Subcategory: "Euler Irregular primes"
(archival tag id 218599, tag last modified 2018-03-14 05:50:22)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 859
Subcategory: "ECPP"
(archival tag id 218600, tag last modified 2019-06-02 14:20:07)

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.

Thomas Ritschel writes (6 Feb 2017): 
Certificate available from here.

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11]
Primality testing 6284333378...0773653189 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.22% and helper 0.06% (0.73% proof)

6284333378...0773653189 is Fermat and Lucas PRP! (0.4022s+0.0005s)
[Elapsed time: 1.00 seconds]
modified2017-03-31 15:53:57
created2017-02-06 05:13:02

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