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(48375) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part, APR-CL assisted Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): F3 : Water, Broadhurst, VFYPR Decimal Digits: 2634   (log10 is 2633.24426714973) Rank (*): 57021 (digit rank is 2) Entrance Rank (*): 25862 Currently on list? (*): short Submitted: 6/15/2001 10:18:33 CDT Last modified: 6/15/2001 10:18:33 CDT Database id: 30248 Status Flags: Verify Score (*): 28.2944 (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.

APR-CL assisted (tolerated *)

Prime on list: no, rank 16
Subcategory: "APR-CL assisted"
(archival tag id 175584, tag last modified 2003-11-01 21:20:02)

Lucas Aurifeuillian primitive part (archivable *)

Prime on list: yes, rank 15
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 175583, tag last modified 2009-06-28 19:50:24)

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 (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 30248 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Running N-1 test using base 19 Primality testing primB(48375) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 37, base 14+sqrt(37) Calling N-1 BLS with factored part 2.25% and helper 0.45% (7.21% proof) primB(48375) is Fermat and Lucas PRP! (77.890000 seconds) modified 2003-03-25 11:22:47 created 2003-01-07 10:53:04 id 64123