U(6584, - 1, 5039)
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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(6584, - 1, 5039)
Verification status (*):PRP
Official Comment:Generalized Lucas number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x23 : Renze, Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:19238   (log10 is 19237.551774728)
Rank (*):64666 (digit rank is 1)
Entrance Rank (*):25939
Currently on list? (*):short
Submitted:4/18/2007 05:36:15 CDT
Last modified:4/18/2007 05:55:57 CDT
Database id:80075
Status Flags:Verify
Score (*):34.466 (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 7
Subcategory: "Generalized Lucas Number"
(archival tag id 192282, tag last modified 2014-09-17 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.

David Broadhurst writes (11 Sep 2014): 

CHG proof at 19238 digits and 28.18% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/b5039p.zip and a certificate compressed to 3MB in http://physics.open.ac.uk/~dbroadhu/cert/b5039p_cert.gp.gz

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.
fieldvalue
prime_id80075
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"lucasU(6584,-1,5039)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
lucas
trial factoring to 5820317
lucasU(6584,-1,5039) has no small factor.
[Elapsed time: 9.564 seconds]
modified2007-04-21 22:36:36
created2007-04-18 05:52:02
id89259

fieldvalue
prime_id80075
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"lucasU(6584,-1,5039)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing lucasU(6584,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 37
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
127820 bit request FFT size=(7168,18)
Running N+1 test using discriminant 43, base 12+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
127828 bit request FFT size=(7168,18)
Calling N-1 BLS with factored part 1.57% and helper 0.41% (5.12% proof)
lucasU(6584,-1,5039) is Fermat and Lucas PRP! (175.1400s+0.0100s)
[Elapsed time: 175 seconds]
modified2007-04-21 22:36:36
created2007-04-18 05:53:02
id89261

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.