4410546 · Bern(5526)/9712202742835546740714595866405369616019

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:4410546 · Bern(5526)/9712202742835546740714595866405369616019
Verification status (*):PRP
Official Comment (*):Irregular,ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c63 : Ritschel, TOPS, Primo
Decimal Digits:13840   (log10 is 13839.137773079)
Rank (*):78657 (digit rank is 3)
Entrance Rank (*):69134
Currently on list? (*):short
Submitted:4/23/2018 09:03:34 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:124643
Status Flags:Verify
Score (*):33.4467 (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.
Irregular Primes (archivable *)
Prime on list: yes, rank 6
Subcategory: "Irregular Primes"
(archival tag id 219141, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 192
Subcategory: "ECPP"
(archival tag id 219142, tag last modified 2024-07-11 00:37:12)

User comments about this prime (disclaimer):

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Thomas Ritschel writes (23 Apr 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 (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 1373324219...0047234967 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.17% proof) 1373324219...0047234967 is Fermat and Lucas PRP! (14.3727s+0.0024s) [Elapsed time: 14.00 seconds]
modified2020-07-07 22:30:15
created2018-04-23 09:10:46

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.
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