(229473 - 1)/(5613392570256862943 · 24876264677503329001)

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.

Description:(229473 - 1)/(5613392570256862943 · 24876264677503329001)
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c59 : Metcalfe, OpenPFGW, Primo
Decimal Digits:8835   (log10 is 8834.1120516201)
Rank (*):78895 (digit rank is 2)
Entrance Rank (*):62238
Currently on list? (*):short
Submitted:9/6/2012 05:27:52 CDT
Last modified:9/6/2012 05:50:29 CDT
Database id:109153
Status Flags:Verify
Score (*):32.0558 (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 251
Subcategory: "ECPP"
(archival tag id 214522, tag last modified 2021-09-18 09:37:41)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 14
Subcategory: "Mersenne cofactor"
(archival tag id 214523, tag last modified 2021-02-24 00:50:28)

User comments about this prime (disclaimer):

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David Metcalfe writes (11 Sep 2014):  (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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(2^29473-1)/(5613392570256862943*24876264677503329001)" 2>&1 PFGW Version [GWNUM 26.5] (2^29473-1)/(561....264677503329001) 1/1 mro=0 trial factoring to 2512903 (2^29473-1)/(5613392570256862943*24876264677503329001) has no small factor. [Elapsed time: 2.157 seconds]
modified2020-07-07 17:30:24
created2012-09-06 05:35:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"(2^29473-1)/(5613392570256862943*24876264677503329001)" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (2^29473-1)/(5613392570256862943*24876264677503329001) [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 0.09% and helper 0.06% (0.32% proof) (2^29473-1)/(5613392570256862943*24876264677503329001) is Fermat and Lucas PRP! (29.8086s+0.0205s) [Elapsed time: 30.00 seconds]
modified2020-07-07 17:30:24
created2012-09-06 05:46:33

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
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