
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(1599,  1, 5039) 
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:  16141 (log_{10} is 16140.98941593) 
Rank (*):  67398 (digit rank is 1) 
Entrance Rank (*):  27633 
Currently on list? (*):  short 
Submitted:  4/18/2007 05:50:47 CDT 
Last modified:  4/18/2007 06:20:16 CDT 
Database id:  80076 
Status Flags:  Verify 
Score (*):  33.923 (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 10
Subcategory: "Generalized Lucas Number"
(archival tag id 192445, tag last modified 20140917 12:50:32)
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.
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  80076 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"lucasU(1599,1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] lucas trial factoring to 4817626 lucasU(1599,1,5039) has no small factor. [Elapsed time: 6.802 seconds]

modified  20070421 22:36:36 
created  20070418 05:52:12 
id  89260 

field  value 
prime_id  80076 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"lucasU(1599,1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(1599,1,5039) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 37 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) 107248 bit request FFT size=(6144,18) Running N1 test using base 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) 107248 bit request FFT size=(6144,18) Running N+1 test using discriminant 67, base 15+sqrt(67) 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) 107256 bit request FFT size=(6144,18) Calling N1 BLS with factored part 1.73% and helper 0.48% (5.65% proof) lucasU(1599,1,5039) is Fermat and Lucas PRP! (149.8900s+0.0000s) [Elapsed time: 150 seconds]

modified  20070421 22:36:36 
created  20070418 05:55:57 
id  89262 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
