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: V(8807)/356419291 Verification status (*): PRP Official Comment: Lucas cofactor Proof-code(s): (*): c8 : Water, Broadhurst, Primo Decimal Digits: 1833   (log10 is 1832.00218648) Rank (*): 84659 (digit rank is 5) Entrance Rank (*): 43987 Currently on list? (*): no Submitted: 3/7/2004 05:40:44 CDT Last modified: 3/7/2004 05:40:44 CDT Database id: 69400 Status Flags: Verify Score (*): 27.1635 (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 cofactor (archivable *)

Prime on list: no, rank 24
Subcategory: "Lucas cofactor"
(archival tag id 179923, tag last modified 2013-05-19 13:50:30)

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 69400 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"V(8807)/356419291" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing V(8807)/356419291 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 454052 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 12180 bit request FFT size=(768,16) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 12188 bit request FFT size=(768,16) Calling N-1 BLS with factored part 0.49% and helper 0.13% (1.66% proof) V(8807)/356419291 is Fermat and Lucas PRP! (5.5903s+0.0212s) modified 2004-04-13 09:53:22 created 2004-03-07 05:54:16 id 74351