U(19258, - 1, 5039)

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Description:U(19258, - 1, 5039)
Verification status (*):PRP
Official Comment (*):Generalized Lucas number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x23 : Broadhurst, Water, Renze, OpenPFGW, Primo
Decimal Digits:21586   (log10 is 21585.871142678)
Rank (*):67725 (digit rank is 1)
Entrance Rank (*):24366
Currently on list? (*):short
Submitted:4/22/2007 13:04:14 CDT
Last modified:4/22/2007 13:27:57 CDT
Database id:80154
Status Flags:Verify
Score (*):34.8223 (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 14
Subcategory: "Generalized Lucas Number"
(archival tag id 192115, tag last modified 2021-08-03 03:37:35)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 May 2021):  (report abuse)
CHG proof at 21586 digits and 28.37% factorization.

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_id80154
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"lucasU(19258,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] lucas trial factoring to 6588625 lucasU(19258,-1,5039) has no small factor. [Elapsed time: 12.123 seconds]
modified2020-07-07 17:30:41
created2007-04-22 13:22:01
id89417

fieldvalue
prime_id80154
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"lucasU(19258,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(19258,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 53 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) 143422 bit request FFT size=(8192,18) 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) 143422 bit request FFT size=(8192,18) Running N-1 test using base 67 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) 143422 bit request FFT size=(8192,18) Running N+1 test using discriminant 79, base 20+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) 143430 bit request FFT size=(8192,18) Calling N-1 BLS with factored part 1.24% and helper 0.48% (4.21% proof) lucasU(19258,-1,5039) is Fermat and Lucas PRP! (294.8400s+0.0100s) [Elapsed time: 295 seconds]
modified2020-07-07 17:30:41
created2007-04-22 13:23:02
id89418

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
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