- E(1466)/167900532276654417372106952612534399239

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(1466)/167900532276654417372106952612534399239
Verification status (*):PRP
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:3682   (log10 is 3681.226989923)
Rank (*):94430 (digit rank is 2)
Entrance Rank (*):73128
Currently on list? (*):short
Submitted:2/16/2013 18:13:36 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:111260
Blob database id:296
Status Flags:Verify
Score (*):29.3373 (normalized score 0)

Description: (from blob table id=296)

[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 16
Subcategory: "Euler Irregular primes"
(archival tag id 215087, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 682
Subcategory: "ECPP"
(archival tag id 215088, tag last modified 2024-07-11 00:37:12)

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):  (report abuse)

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] 1686513892468376....9459544889014799 1/1 mro=0 trial factoring to 972159 1686513892...4889014799 has no small factor. [Elapsed time: 1.632 seconds]
modified2020-07-07 22:30:22
created2013-02-16 18:18:05

machineRedHat P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 1686513892...4889014799 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.38% and helper 0.13% (1.30% proof) 1686513892...4889014799 is Fermat and Lucas PRP! (6.9821s+0.0022s) [Elapsed time: 7.00 seconds]
modified2020-07-07 22:30:22
created2013-02-16 18:20:10

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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