- E(1990)/83382\

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description: - E(1990)/83382\
Verification status (*):PRP
Official Comment (*):Euler irregular, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:5258   (log10 is 5257.4254198007)
Rank (*):90787 (digit rank is 3)
Entrance Rank (*):69548
Currently on list? (*):short
Submitted:2/16/2013 18:07:33 UTC
Last modified:3/11/2023 15:54:10 UTC
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 13
Subcategory: "Euler Irregular primes"
(archival tag id 215085, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 549
Subcategory: "ECPP"
(archival tag id 215086, tag last modified 2024-07-11 00:37:12)

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.
machineRedHat P4 P4
notesPFGW Version [GWNUM 26.5] 2663298231573503....0656816516908917 1/1 mro=0 trial factoring to 1432002 2663298231...6516908917 has no small factor. [Elapsed time: 3.244 seconds]
modified2020-07-07 22:30:22
created2013-02-16 18:18:01

machineRedHat P4 P4
notesPFGW Version [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]
modified2020-07-07 22:30:22
created2013-02-16 18:19:56

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