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(45565) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part, ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c4 : Broadhurst, Primo Decimal Digits: 3512   (log10 is 3511.6176367337) Rank (*): 54793 (digit rank is 7) Entrance Rank (*): 50490 Currently on list? (*): short Submitted: 2/2/2009 11:51:14 CDT Last modified: 2/2/2009 12:20:38 CDT Database id: 86496 Status Flags: Verify Score (*): 29.1905 (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 10
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 186995, tag last modified 2009-06-28 19:50:24)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 190
Subcategory: "ECPP"
(archival tag id 186996, tag last modified 2009-11-14 14:20:22)

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 (2 Feb 2009): 

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 86496 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 4146070988...4285301763.........5441787138242053 1/1 trial factoring to 923551 4146070988...3815282001 has no small factor. [Ellapsed time: 1.485 seconds] modified 2009-02-05 12:51:34 created 2009-02-02 11:52:01 id 102416

field value prime_id 86496 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 4146070988...3815282001 [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) 23340 bit request FFT size=(1536,16) Running N-1 test using base 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) 23340 bit request FFT size=(1536,16) Running N+1 test using discriminant 41, base 12+sqrt(41) 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) 23348 bit request FFT size=(1536,16) Calling N-1 BLS with factored part 1.55% and helper 0.19% (4.86% proof) 4146070988...3815282001 is Fermat and Lucas PRP! (6.3500s+0.0000s) [Elapsed time: 7.00 seconds] modified 2009-02-02 11:53:08 created 2009-02-02 11:53:01 id 102418