U(11200, - 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(11200, - 1, 5039)
Verification status (*):PRP
Official Comment:Generalized Lucas number, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:20400   (log10 is 20399.9604156515)
Rank (*):63363 (digit rank is 1)
Entrance Rank (*):14936
Currently on list? (*):short
Submitted:3/9/2004 09:09:50 CDT
Last modified:3/9/2004 09:09:50 CDT
Database id:69430
Status Flags:Verify
Score (*):34.6475 (normalized score 0.0001)

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.
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 3
Subcategory: "Cyclotomy Proof"
(archival tag id 192169, tag last modified 2009-02-12 20:01:27)
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 5
Subcategory: "Generalized Lucas Number"
(archival tag id 192168, 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): 
WL proof

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_id69430
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"lucasU(11200,-1,5039)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing lucasU(11200,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 6199893
Running N-1 test using base 37
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(8192,21) to FFT(8192,20)
Reduced from FFT(8192,20) to FFT(8192,19)
Reduced from FFT(8192,19) to FFT(8192,18)
Reduced from FFT(8192,18) to FFT(8192,17)
135544 bit request FFT size=(8192,17)
Running N-1 test using base 59
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(8192,21) to FFT(8192,20)
Reduced from FFT(8192,20) to FFT(8192,19)
Reduced from FFT(8192,19) to FFT(8192,18)
Reduced from FFT(8192,18) to FFT(8192,17)
135544 bit request FFT size=(8192,17)
Running N-1 test using base 61
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(8192,21) to FFT(8192,20)
Reduced from FFT(8192,20) to FFT(8192,19)
Reduced from FFT(8192,19) to FFT(8192,18)
Reduced from FFT(8192,18) to FFT(8192,17)
135544 bit request FFT size=(8192,17)
Running N+1 test using discriminant 79, base 16+sqrt(79)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(8192,21) to FFT(8192,20)
Reduced from FFT(8192,20) to FFT(8192,19)
Reduced from FFT(8192,19) to FFT(8192,18)
Reduced from FFT(8192,18) to FFT(8192,17)
135552 bit request FFT size=(8192,17)
Calling N-1 BLS with factored part 1.24% and helper 0.26% (3.97% proof)
lucasU(11200,-1,5039) is Fermat and Lucas PRP! (559.4009s+0.0258s)
modified2004-04-13 09:53:22
created2004-03-09 09:23:00
id74383

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.