- E(1142)/6233437695283865492412648122\

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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(1142)/6233437695283865492412648122\
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:2697   (log10 is 2696.159629936)
Rank (*):88985 (digit rank is 1)
Entrance Rank (*):82362
Currently on list? (*):short
Submitted:4/18/2015 17:08:15 CDT
Last modified:4/20/2015 07:50:19 CDT
Database id:119774
Blob database id:337
Status Flags:Verify, TrialDiv
Score (*):28.368 (normalized score 0)

Description: (from blob table id=337)

[This prime has a pre-calculated decimal expansion (linked blob)]

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 13
Subcategory: "Euler Irregular primes"
(archival tag id 217989, tag last modified 2018-03-14 05:50:22)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 620
Subcategory: "ECPP"
(archival tag id 217990, 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.

Serge Batalov writes (18 Apr 2015): 
Certificate at FactorDB

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: WinXP Dual Core 2.6GHz 64-bit Laptop
notesCommand: pfgw64.exe -tc p_119774.txt 2>&1
PFGW Version [GWNUM 27.8]
Primality testing 1444208630...7870043529 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 11+sqrt(11)
Calling N-1 BLS with factored part 0.31% and helper 0.09% (1.05% proof)
1444208630...7870043529 is Fermat and Lucas PRP! (0.7897s+0.0542s)
[Elapsed time: 1 seconds]
modified2015-04-20 07:32:09
created2015-04-20 07:31:20

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.