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: primV(20384, 1, 5281) Verification status (*): PRP Official Comment: Generalized Lucas primitive part, cyclotomy Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x25 : Water, Broadhurst, Primo, OpenPFGW Decimal Digits: 22754   (log10 is 22753.04808274) Rank (*): 34362 (digit rank is 2) Entrance Rank (*): 10116 Currently on list? (*): short Submitted: 4/23/2003 07:08:03 CDT Last modified: 4/23/2003 07:08:03 CDT Database id: 64490 Status Flags: Verify Score (*): 34.9851 (normalized score 0.0035)

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 primitive part (archivable *)

Prime on list: yes, rank 20
Subcategory: "Generalized Lucas primitive part"
(archival tag id 192058, tag last modified 2009-02-12 20:01:29)

Cyclotomy Proof (tolerated *)

Prime on list: no, rank 2
Subcategory: "Cyclotomy Proof"
(archival tag id 192057, tag last modified 2009-02-12 20:01:27)

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 (26 Nov 2005): 

first non-trivial Lenstra proof above 20000 digits

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 64490 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 7 Primality testing primV(20384,1,5281) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N+1 test using discriminant 47, base 3+sqrt(47) Calling N-1 BLS with factored part 1.21% and helper 0.23% (3.88% proof) primV(20384,1,5281) is Fermat and Lucas PRP! (773.010000 seconds) modified 2003-07-12 13:12:12 created 2003-04-24 07:22:55 id 69360