
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(11194,  11195, 3361) 
Verification status (*):  Proven 
Official Comment:  Generalized Lucas number 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x25 : Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  13605 (log_{10} is 13604.7209302) 
Rank (*):  69467 (digit rank is 1) 
Entrance Rank (*):  19710 
Currently on list? (*):  short 
Submitted:  1/28/2004 07:36:58 CDT 
Last modified:  1/28/2004 07:36:58 CDT 
Database id:  68567 
Status Flags:  none 
Score (*):  33.3938 (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 17
Subcategory: "Generalized Lucas Number"
(archival tag id 192878, tag last modified 20160502 05:50:25)
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.
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  68567 
person_id  9 
machine  Linux P4 2.8GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw f tc q"lucasU(11194,11195,3361)" hdls11195.fac 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(11194,11195,3361) [N1/N+1, BrillhartLehmerSelfridge] Reading factors from helper file dls11195.fac trial factoring to 4006474 Running N1 test using base 19 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) 90396 bit request FFT size=(6144,16) Running N+1 test using discriminant 47, base 3+sqrt(47) 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) 90404 bit request FFT size=(6144,16) Calling N1 BLS with factored part 40.07% and helper 0.00% (120.20% proof) lucasU(11194,11195,3361) is prime! (168.7486s+0.0144s)

modified  20050704 09:12:07 
created  20050704 08:54:19 
id  80060 

Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
