U(475, - 1, 5039)
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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(475, - 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:13486   (log10 is 13485.1921007)
Rank (*):69121 (digit rank is 2)
Entrance Rank (*):19247
Currently on list? (*):short
Submitted:12/29/2003 14:49:12 CDT
Last modified:12/29/2003 14:49:12 CDT
Database id:67876
Status Flags:Verify
Score (*):33.3664 (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.
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 20
Subcategory: "Cyclotomy Proof"
(archival tag id 193026, tag last modified 2009-02-12 20:01:27)
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 19
Subcategory: "Generalized Lucas Number"
(archival tag id 193025, 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.

David Broadhurst writes (11 Sep 2014): 
notes

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_id67876
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"lucasU(475,-1,5039)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing lucasU(475,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 3968513
Running N-1 test using base 31
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)
89602 bit request FFT size=(6144,16)
Running N-1 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)
Reduced from FFT(6144,18) to FFT(6144,17)
Reduced from FFT(6144,17) to FFT(6144,16)
89602 bit request FFT size=(6144,16)
Running N-1 test using base 53
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)
89602 bit request FFT size=(6144,16)
Running N-1 test using base 79
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)
89602 bit request FFT size=(6144,16)
Running N-1 test using base 97
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)
89602 bit request FFT size=(6144,16)
Running N+1 test using discriminant 103, base 3+sqrt(103)
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)
89610 bit request FFT size=(6144,16)
Calling N-1 BLS with factored part 1.75% and helper 0.75% (6.01% proof)
lucasU(475,-1,5039) is Fermat and Lucas PRP! (521.4483s+0.2574s)
modified2004-01-16 11:28:34
created2003-12-29 14:53:01
id72814

Query times: 0.0005 seconds to select prime, 0.0003 seconds to seek comments.