(V(28138, 1, 7587) - 1)/(V(28138, 1, 27) - 1)

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:(V(28138, 1, 7587) - 1)/(V(28138, 1, 27) - 1)
Verification status (*):PRP
Official Comment (*):Lehmer primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x45 : Batalov, OpenPFGW, Primo, Unknown
Decimal Digits:33637   (log10 is 33636.656779128)
Rank (*):66161 (digit rank is 1)
Entrance Rank (*):58508
Currently on list? (*):short
Submitted:8/25/2019 20:51:38 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:129880
Status Flags:Verify
Score (*):36.1932 (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.
Lehmer primitive part (archivable *)
Prime on list: yes, rank 2
Subcategory: "Lehmer primitive part"
(archival tag id 223511, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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Serge Batalov writes (26 Aug 2019):  (report abuse)
Proof with factored part 30.05%, with p5513 proven with Primo

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_id129880
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(lucasV(28138,1,7587)-1)/(lucasV(28138,1,27)-1)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (lucasV(28138,1,7587)-1)/(lucasV(28138,1,27)-1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 37 Running N-1 test using base 43 Running N-1 test using base 59 Running N-1 test using base 101 Running N-1 test using base 137 Running N-1 test using base 139 Running N+1 test using discriminant 157, base 3+sqrt(157) Calling N-1 BLS with factored part 1.18% and helper 0.03% (3.56% proof) (lucasV(28138,1,7587)-1)/(lucasV(28138,1,27)-1) is Fermat and Lucas PRP! (213.5472s+0.0031s) [Elapsed time: 3.57 minutes]
modified2020-07-07 22:30:11
created2019-08-25 20:53:01
id175565

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