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: Phi(3273, - 100) Verification status (*): PRP Official Comment: Unique, ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c8 : Water, Broadhurst, Primo Decimal Digits: 4361   (log10 is 4360.00432093949) Rank (*): 82439 (digit rank is 2) Entrance Rank (*): 28555 Currently on list? (*): short Submitted: 4/7/2003 13:46:57 CDT Last modified: 4/7/2003 13:46:57 CDT Database id: 64312 Status Flags: Verify Score (*): 29.8635 (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.

Unique (archivable *)

Prime on list: yes, rank 20
Subcategory: "Unique"
(archival tag id 210384, tag last modified 2014-05-20 07:51:28)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 424
Subcategory: "ECPP"
(archival tag id 210383, tag last modified 2017-09-09 11:20:24)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): 

certificate

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.

field value prime_id 64312 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(3273,-100) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 0.79% Phi(3273,-100) is PRP! (4.640000 seconds) modified 2003-04-08 07:42:59 created 2003-04-08 07:42:50 id 69181