(23539 + 1)/3
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The hardware and software on this system was updated September 4th.  Please let me know of any problem you encounter. <caldwell@utm.edu>

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:(23539 + 1)/3
Verification status (*):PRP
Official Comment:First titanic by ECPP, generalized Lucas number, Wagstaff
Proof-code(s): (*):M : Morain
Decimal Digits:1065   (log10 is 1064.86803340011)
Rank (*):106060 (digit rank is 8)
Entrance Rank (*):838
Currently on list? (*):short
Submitted:1989
Last modified:1989
Database id:54344
Status Flags:Verify
Score (*):25.4686 (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.
Generalized Lucas Number (archivable *)
Prime on list: no, rank 96
Subcategory: "Generalized Lucas Number"
(archival tag id 181330, tag last modified 2014-09-17 12:50:32)
* old special cases (deprecated *)
Prime on list: no, rank 1
Subcategory: "* old special cases"
(archival tag id 181329, tag last modified 2005-06-03 13:39:34)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 821
Subcategory: "ECPP"
(archival tag id 181331, tag last modified 2014-09-17 12:50:31)
Wagstaff (archivable *)
Prime on list: yes, rank 9
Subcategory: "Wagstaff"
(archival tag id 181332, tag last modified 2014-09-17 12:50:33)

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.
fieldvalue
prime_id54344
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (2^3539+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) Running N+1 test using discriminant 13, base 6+sqrt(13) Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N+1 BLS with factored part 2.69% and helper 1.33% (9.44% proof) (2^3539+1)/3 is Fermat and Lucas PRP! (46.500000 seconds)
modified2003-03-25 11:23:04
created2003-01-03 23:43:33
id60765

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.