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: primA(82975) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p54 : Water, Broadhurst, OpenPFGW Decimal Digits: 6935   (log10 is 6934.29545852301) Rank (*): 48329 (digit rank is 3) Entrance Rank (*): 17982 Currently on list? (*): short Submitted: 7/7/2001 11:18:36 CDT Last modified: 7/7/2001 11:18:36 CDT Database id: 21561 Status Flags: Verify Score (*): 31.3046 (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.

Lucas Aurifeuillian primitive part (archivable *)

Prime on list: yes, rank 1
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 194738, tag last modified 2009-02-12 20:01:29)

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): 

notes

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 21561 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 1974506296...6187119345 Running N-1 test using base 2 1193072744...6290940501 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 37, base 3+sqrt(37) Calling N-1 BLS with factored part 1.45% and helper 0.07% (4.42% proof) primA(82975) is Fermat and Lucas PRP! (1060.950000 seconds) modified 2003-03-25 11:22:43 created 2003-01-08 12:49:36 id 64625