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: U(2783, - 1, 3779) Verification status (*): PRP Official Comment: Generalized Lucas number Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): CH3 : Water, Broadhurst, CHG, Primo, OpenPFGW Decimal Digits: 13014   (log10 is 13013.3711053197) Rank (*): 60618 (digit rank is 6) Entrance Rank (*): 26742 Currently on list? (*): short Submitted: 9/22/2005 16:12:22 CDT Last modified: 11/19/2005 16:05:11 CDT Database id: 75679 Status Flags: Verify Score (*): 33.2561 (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.

Generalized Lucas Number (archivable *)

Prime on list: yes, rank 19
Subcategory: "Generalized Lucas Number"
(archival tag id 193440, tag last modified 2013-01-10 05:50:32)

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.

Chris Caldwell writes (19 Nov 2005): 

CHG proof with ECPP helpers. Certificate of proof may be found here: http://physics.open.ac.uk/~dbroadhu/cert/b3779b.zip

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 75679 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(2783,-1,3779)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(2783,-1,3779) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 3818917 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 86468 bit request FFT size=(6144,16) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 86468 bit request FFT size=(6144,16) Running N+1 test using discriminant 59, base 14+sqrt(59) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 86476 bit request FFT size=(6144,16) Calling N-1 BLS with factored part 1.33% and helper 0.75% (4.74% proof) lucasU(2783,-1,3779) is Fermat and Lucas PRP! (266.3706s+0.0041s) [Elapsed time: 267 seconds] modified 2005-09-23 12:19:27 created 2005-09-22 16:42:00 id 80856