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(42685) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c46 : Boncompagni, Primo Decimal Digits: 3568   (log10 is 3567.213576943) Rank (*): 54690 (digit rank is 1) Entrance Rank (*): 49271 Currently on list? (*): short Submitted: 7/7/2008 12:15:10 CDT Last modified: 7/8/2008 10:36:54 CDT Database id: 85278 Status Flags: Verify Score (*): 29.2394 (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 9
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 186051, 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.

Bernardo Boncompagni writes (9 Jul 2008): 

Please find here a zipped Primo certificate.

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 85278 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 1635222834...2030593542.........4254638616426807 1/1 trial factoring to 939503 1635222834...7896617351 has no small factor. [Ellapsed time: 1.489 seconds] modified 2008-07-08 10:47:48 created 2008-07-08 10:05:02 id 100017

field value prime_id 85278 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1635222834...7896617351 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) Reduced from FFT(1536,17) to FFT(1536,16) 23710 bit request FFT size=(1536,16) Running N+1 test using discriminant 17, base 1+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) Reduced from FFT(1536,17) to FFT(1536,16) 23718 bit request FFT size=(1536,16) Calling N-1 BLS with factored part 2.72% and helper 0.13% (8.28% proof) 1635222834...7896617351 is Fermat and Lucas PRP! (5.4700s+0.0000s) [Elapsed time: 5.00 seconds] modified 2008-07-08 10:36:54 created 2008-07-08 10:36:49 id 100023