primV(42, - 1, 23376)

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This prime's information:

Description:primV(42, - 1, 23376)
Verification status (*):PRP
Official Comment (*):Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x23 : Broadhurst, Water, Renze, OpenPFGW, Primo
Decimal Digits:25249   (log10 is 25248.598594475)
Rank (*):71168 (digit rank is 1)
Entrance Rank (*):24986
Currently on list? (*):short
Submitted:9/19/2007 16:06:32 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:82297
Status Flags:Verify
Score (*):35.3068 (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 primitive part (archivable *)
Prime on list: yes, rank 19
Subcategory: "Generalized Lucas primitive part"
(archival tag id 191772, tag last modified 2023-03-11 15:53:59)

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 (12 May 2021):  (report abuse)
CHG proof, at 26.38% factorization, helped by a BLS proof of primV(42,-1,3888).

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_id82297
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"primV(42,-1,23376)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 7798691 primV(42,-1,23376) has no small factor. [Elapsed time: 16.666 seconds]
modified2020-07-07 22:30:40
created2007-09-19 16:22:02
id93709

fieldvalue
prime_id82297
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"primV(42,-1,23376)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing primV(42,-1,23376) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167758 bit request FFT size=(10240,17) Running N-1 test using base 37 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167758 bit request FFT size=(10240,17) Running N+1 test using discriminant 43, base 18+sqrt(43) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) 167766 bit request FFT size=(10240,17) Calling N-1 BLS with factored part 0.69% and helper 0.03% (2.09% proof) primV(42,-1,23376) is Fermat and Lucas PRP! (356.5400s+0.1100s) [Elapsed time: 6.07 minutes]
modified2020-07-07 22:30:40
created2007-09-19 16:23:01
id93710

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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