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(52825) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x25 : Water, Broadhurst, Primo, OpenPFGW Decimal Digits: 4414   (log10 is 4413.72986153476) Rank (*): 53485 (digit rank is 4) Entrance Rank (*): 28800 Currently on list? (*): short Submitted: 5/11/2003 10:30:50 CDT Last modified: 5/11/2003 10:30:50 CDT Database id: 64671 Status Flags: Verify Score (*): 29.9016 (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 5
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 195445, 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): 

helper for KP

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 64671 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 5368606028...7587871688Reading factors from helper file helper Running N-1 test using base 2 1890648007...8863495651 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 30.13% and helper 0.30% (90.68% proof) 5368606028...8863495651 is Fermat and Lucas PRP! (23.040000 seconds) Helper File: 2 5 5 13 641 1049 1087 1447 2113 4481 5737 35201 141961 2563969 75440641 75518783 683478401 1435815041 5072305921 11862575248703 42311526823103 5326379933318401 31187396775005101 35323750923943681 499750037222722721 8132307034170126721 3891324187650256896001 878132240443974874201601 2211745416606187093767661 1271150843287904563935054721 2811666624525811646469915877 471991644996070811213117005172115579281 1931734634522754726108707718410439174358483201 316837008400107576629115441641182686718784605974069121 717183675566658213132761730294626635650067479275923957352582406983301023453681347576121 12948849060334671674592757616583288...(91 digits)...66918228225397498956629185213102721 48036584363254825202976389156102973...(694 digits)...24688840773271110628749178344879721 modified 2005-12-30 08:30:48 created 2003-05-11 18:27:09 id 69527