- E(5186)/295970922359784619239409649676896529941379763

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(5186)/295970922359784619239409649676896529941379763
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:15954   (log10 is 15953.682718292)
Rank (*):76711 (digit rank is 1)
Entrance Rank (*):67149
Currently on list? (*):short
Submitted:3/14/2018 10:19:13 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:124523
Status Flags:Verify
Score (*):33.8868 (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 7
Subcategory: "Euler Irregular primes"
(archival tag id 219082, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 155
Subcategory: "ECPP"
(archival tag id 219083, 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.

Thomas Ritschel writes (14 Mar 2018):  (report abuse)
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 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 4816352807...8430556347 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.21% proof) 4816352807...8430556347 is Fermat and Lucas PRP! (16.8420s+0.0793s) [Elapsed time: 17.00 seconds]
modified2020-07-07 22:30:15
created2018-03-14 10:21:09

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.