- E(1990)/83382\
08577950624722417016286765473477033741642105671913

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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(1990)/83382\
08577950624722417016286765473477033741642105671913
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:5258   (log10 is 5257.4254198007)
Rank (*):79927 (digit rank is 3)
Entrance Rank (*):69548
Currently on list? (*):short
Submitted:2/16/2013 12:07:33 CDT
Last modified:2/16/2013 12:21:14 CDT
Database id:111259
Blob database id:295
Status Flags:Verify
Score (*):30.4451 (normalized score 0)

Description: (from blob table id=295)

[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 6
Subcategory: "Euler Irregular primes"
(archival tag id 215085, tag last modified 2014-06-21 13:51:45)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 372
Subcategory: "ECPP"
(archival tag id 215086, tag last modified 2017-10-19 05:50:25)

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.

David Broadhurst writes (11 Sep 2014): 
certificate

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_id111259
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
2663298231573503....0656816516908917 1/1 mro=0


trial factoring to 1432002
2663298231...6516908917 has no small factor.
[Elapsed time: 3.244 seconds]
modified2013-02-24 16:44:13
created2013-02-16 12:18:01
id152792

fieldvalue
prime_id111259
person_id9
machineRedHat P4 P4
whatprp
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 2663298231...6516908917 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N-1 BLS with factored part 0.25% and helper 0.06% (0.83% proof)
2663298231...6516908917 is Fermat and Lucas PRP! (13.7789s+0.0016s)
[Elapsed time: 14.00 seconds]
modified2013-02-16 12:20:10
created2013-02-16 12:19:56
id152794

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