U(2219, - 1, 4049)
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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(2219, - 1, 4049)
Verification status (*):PRP
Official Comment:Generalized Lucas number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH3 : Water, Broadhurst, Primo, OpenPFGW, CHG
Decimal Digits:13546   (log10 is 13545.2451163814)
Rank (*):68953 (digit rank is 1)
Entrance Rank (*):26151
Currently on list? (*):short
Submitted:10/4/2005 10:55:10 CDT
Last modified:11/20/2005 08:23:18 CDT
Database id:75823
Status Flags:Verify
Score (*):33.3802 (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 18
Subcategory: "Generalized Lucas Number"
(archival tag id 192959, tag last modified 2016-05-02 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.

Chris Caldwell writes (11 Sep 2014): 
CHG proof with ECPP helpers. For certificate of proof see http://physics.open.ac.uk/~dbroadhu/cert/b4049a.zip

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_id75823
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"lucasU(2219,-1,4049)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing lucasU(2219,-1,4049) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 3987634
Running N-1 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)
90002 bit request FFT size=(6144,16)
Running N-1 test using base 17
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)
90002 bit request FFT size=(6144,16)
Running N+1 test using discriminant 37, base 12+sqrt(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)
Reduced from FFT(6144,18) to FFT(6144,17)
Reduced from FFT(6144,17) to FFT(6144,16)
90010 bit request FFT size=(6144,16)
Calling N-1 BLS with factored part 0.98% and helper 0.56% (3.50% proof)
lucasU(2219,-1,4049) is Fermat and Lucas PRP! (250.7310s+0.0144s)
[Elapsed time: 251 seconds]
modified2005-10-05 19:02:33
created2005-10-04 11:23:00
id81009

Query times: 0.0004 seconds to select prime, 0.0002 seconds to seek comments.