U(11200, - 1, 5039)

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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 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:20400   (log10 is 20399.960415652)
Rank (*):68085 (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)

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 10
Subcategory: "Cyclotomy Proof"
(archival tag id 192169, tag last modified 2019-06-27 21:50:21)
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 15
Subcategory: "Generalized Lucas Number"
(archival tag id 192168, 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)
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)
modified2020-07-07 17:30:45
created2004-03-09 09:23:00
id74383

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
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