- E(958)/(23041998673 · 60728415169 · 1169782469256830327 · 673624354114927513970319552187639)

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.

Description: - E(958)/(23041998673 · 60728415169 · 1169782469256830327 · 673624354114927513970319552187639)
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:2183   (log10 is 2182.1634874407)
Rank (*):98919 (digit rank is 2)
Entrance Rank (*):97597
Currently on list? (*):short
Submitted:12/19/2020 04:11:33 CDT
Last modified:12/19/2020 04:20:13 CDT
Database id:131487
Status Flags:Verify, TrialDiv
Score (*):27.7089 (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 18
Subcategory: "Euler Irregular primes"
(archival tag id 225761, tag last modified 2020-12-26 21:50:12)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 752
Subcategory: "ECPP"
(archival tag id 225762, tag last modified 2021-10-14 15:37:18)

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 (19 Dec 2020):  (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 (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 29.8] Primality testing 1457093566...2993445381 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.30% and helper 0.28% (1.21% proof) 1457093566...2993445381 is Fermat and Lucas PRP! (0.2655s+0.0003s) [Elapsed time: 0.00 seconds]
modified2021-04-20 17:39:25
created2020-12-19 04:16:02

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.
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