(241681 - 1)/1052945423 / 16647332713153 / 2853686272534246492102086015457

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:(241681 - 1)/1052945423 / 16647332713153 / 2853686272534246492102086015457
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:12495   (log10 is 12494.532092524)
Rank (*):78051 (digit rank is 1)
Entrance Rank (*):66447
Currently on list? (*):short
Submitted:4/26/2015 03:24:12 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:119809
Status Flags:Verify, TrialDiv
Score (*):33.1301 (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 208
Subcategory: "ECPP"
(archival tag id 217994, tag last modified 2023-03-11 16:02:30)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 15
Subcategory: "Mersenne cofactor"
(archival tag id 217995, tag last modified 2023-03-11 16:02:31)

User comments about this prime (disclaimer):

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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"(2^41681-1)/1052945423/16647332713153/2853686272534246492102086015457" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (2^41681-1)/1052945423/16647332713153/2853686272...2086015457 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.17% and helper 0.01% (0.52% proof) (2^41681-1)/1052945423/16647332713153/2853686272...2086015457 is Fermat and Lucas PRP! (10.0084s+0.0003s) [Elapsed time: 10.00 seconds]
modified2020-07-07 22:30:17
created2015-04-26 03:31:01

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