(251487 - 1)/57410994232247 / 17292148963401772464767849635553

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:(251487 - 1)/57410994232247 / 17292148963401772464767849635553
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c77 : Batalov, Primo
Decimal Digits:15455   (log10 is 15454.134542715)
Rank (*):75078 (digit rank is 2)
Entrance Rank (*):67820
Currently on list? (*):short
Submitted:11/5/2018 02:20:19 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:125757
Status Flags:Verify
Score (*):33.7884 (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 136
Subcategory: "ECPP"
(archival tag id 219948, tag last modified 2023-09-17 09:37:11)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 14
Subcategory: "Mersenne cofactor"
(archival tag id 219949, tag last modified 2023-03-11 16:02:31)

User comments about this prime (disclaimer):

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Serge Batalov writes (5 Nov 2018):  (report abuse)
Certificate will be at FactorDB.com

* (currently FactorDB is under repairs for uploading certs)

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
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^51487-1)/57410994232247/17292148963401772464767849635553" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (2^51487-1)/57410994232247/1729214896...7849635553 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 12+sqrt(13) Calling N-1 BLS with factored part 0.11% and helper 0.08% (0.40% proof) (2^51487-1)/57410994232247/1729214896...7849635553 is Fermat and Lucas PRP! (16.1966s+0.0003s) [Elapsed time: 17.00 seconds]
modified2020-07-07 22:30:14
created2018-11-05 02:21:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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