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: primB(34045) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part, ECPP Proof-code(s): (*): c8 : Water, Broadhurst, Primo Decimal Digits: 2584   (log10 is 2583.7057656158) Rank (*): 57340 (digit rank is 3) Entrance Rank (*): 32606 Currently on list? (*): short Submitted: 5/19/2003 08:31:03 CDT Last modified: 5/19/2003 08:31:03 CDT Database id: 64733 Status Flags: Verify Score (*): 28.2353 (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 255
Subcategory: "ECPP"
(archival tag id 175619, tag last modified 2009-11-14 14:20:22)

Lucas Aurifeuillian primitive part (archivable *)

Prime on list: yes, rank 17
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 175618, tag last modified 2009-06-28 19:50:24)

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 64733 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 19 Primality testing 5078852682...9135153201 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 29, base 18+sqrt(29) Calling N-1 BLS with factored part 0.89% and helper 0.35% (3.01% proof) 5078852682...9135153201 is Fermat and Lucas PRP! (5.430000 seconds) modified 2003-07-12 13:12:12 created 2003-05-20 06:40:39 id 69605