primV(38513, - 1, 11502)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:primV(38513, - 1, 11502)
Verification status (*):Proven
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:34668   (log10 is 34667.191565536)
Rank (*):66204 (digit rank is 1)
Entrance Rank (*):16517
Currently on list? (*):short
Submitted:11/13/2006 16:01:18 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:78834
Status Flags:none
Score (*):36.2864 (normalized score 0.0001)

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 6
Subcategory: "Generalized Lucas primitive part"
(archival tag id 190780, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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David Broadhurst writes (12 May 2021):  (report abuse)
BLS proof helped by a CHG proof of primV(38513,-1,1944).

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"primV(38513,-1,11502)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 10963339 primV(38513,-1,11502) has no small factor. [Elapsed time: 31.312 seconds]
modified2020-07-07 22:30:42
created2006-11-13 16:22:02

machineWinXP Pent_M 1.7GHz Laptop
notesCommand: pfgw.exe -n -tc -hhelp.txt -q"primV(38513,-1,11502)" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Reading factors from helper file help.txt Running N-1 test using base 47 Primality testing primV(38513,-1,11502) [N-1/N+1, Brillhart-Lehmer-Selfridge] N-Calling N-1 BLS with factored part 34.46% and helper 0.01% (103.40% proof) primV(38513,-1,11502) is prime! (3819.0341s+0.6583s) 1Running N+1 test using discriminant 67, base 18+sqrt(67) [Elapsed time: 3830 seconds]
modified2020-07-07 22:30:42
created2006-11-15 13:41:49

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