(253381 - 1)/15588960193 / 38922536168186976769 / 155991271597169062945033668006103

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:(253381 - 1)/15588960193 / 38922536168186976769 / 155991271597169062945033668006103
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c84 : Underwood, Primo
Decimal Digits:16008   (log10 is 16007.306079962)
Rank (*):74138 (digit rank is 1)
Entrance Rank (*):65749
Currently on list? (*):short
Submitted:3/8/2017 18:32:25 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:123121
Status Flags:Verify, TrialDiv
Score (*):33.8972 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 123
Subcategory: "ECPP"
(archival tag id 218654, tag last modified 2023-03-11 16:02:30)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 13
Subcategory: "Mersenne cofactor"
(archival tag id 218655, tag last modified 2023-03-11 16:02:31)

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.

Paul Underwood writes (8 Mar 2017):  (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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing (2^53381-1)/15588960193/38922536168186976769/1559912715...3668006103 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 31, base 12+sqrt(31) Calling N-1 BLS with factored part 0.08% and helper 0.02% (0.25% proof) (2^53381-1)/15588960193/38922536168186976769/1559912715...3668006103 is Fermat and Lucas PRP! (16.5925s+0.0663s) [Elapsed time: 17.00 seconds]
modified2020-07-07 22:30:16
created2017-03-08 18:33:01

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