(241521 - 1)/41602235382028197528613357724450752065089

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:(241521 - 1)/41602235382028197528613357724450752065089
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:12459   (log10 is 12458.447333297)
Rank (*):78058 (digit rank is 2)
Entrance Rank (*):58448
Currently on list? (*):short
Submitted:8/21/2012 05:57:18 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:108899
Status Flags:Verify
Score (*):33.1212 (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 209
Subcategory: "ECPP"
(archival tag id 214461, tag last modified 2023-03-11 16:02:30)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 16
Subcategory: "Mersenne cofactor"
(archival tag id 214462, tag last modified 2023-03-11 16:02:31)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(2^41521-1)/41602235382028197528613357724450752065089" 2>&1 PFGW Version [GWNUM 26.5] (2^41521-1)/4160....7724450752065089 1/1 mro=0 trial factoring to 3643482 (2^41521-1)/4160223538...0752065089 has no small factor. [Elapsed time: 5.291 seconds]
modified2020-07-07 22:30:24
created2012-08-21 06:05:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"(2^41521-1)/41602235382028197528613357724450752065089" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (2^41521-1)/4160223538...0752065089 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 41, base 1+sqrt(41) Calling N-1 BLS with factored part 0.09% and helper 0.05% (0.33% proof) (2^41521-1)/4160223538...0752065089 is Fermat and Lucas PRP! (58.9730s+0.0004s) [Elapsed time: 59.00 seconds]
modified2020-07-07 22:30:24
created2012-08-21 06:43:38

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