
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(7537,  7538, 3361) 
Verification status (*):  PRP 
Official Comment:  Generalized Lucas number 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x23 : Renze, Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  13028 (log_{10} is 13027.580549651) 
Rank (*):  69878 (digit rank is 2) 
Entrance Rank (*):  30592 
Currently on list? (*):  short 
Submitted:  3/24/2007 15:49:54 CDT 
Last modified:  3/24/2007 15:54:59 CDT 
Database id:  79819 
Status Flags:  Verify 
Score (*):  33.2595 (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 20
Subcategory: "Generalized Lucas Number"
(archival tag id 193429, tag last modified 20160502 05:50:25)
User comments about this prime (disclaimer):
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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  79819 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"lucasU(7537,7538,3361)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] lucas trial factoring to 3823398 lucasU(7537,7538,3361) has no small factor. [Elapsed time: 4.445 seconds]

modified  20070421 22:36:37 
created  20070324 15:52:01 
id  88749 

field  value 
prime_id  79819 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"lucasU(7537,7538,3361)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(7537,7538,3361) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 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) 86562 bit request FFT size=(6144,16) Running N1 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) 86562 bit request FFT size=(6144,16) Running N+1 test using discriminant 7, base 1+sqrt(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) 86570 bit request FFT size=(6144,16) Calling N1 BLS with factored part 1.47% and helper 0.06% (4.47% proof) lucasU(7537,7538,3361) is Fermat and Lucas PRP! (116.1300s+0.0100s) [Elapsed time: 117 seconds]

modified  20070421 22:36:37 
created  20070324 15:53:02 
id  88750 

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
