(200608377 - 1)/20059

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:(200608377 - 1)/20059
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c67 : Batalov, NewPGen, OpenPFGW, Primo
Decimal Digits:36037   (log10 is 36036.323880311)
Rank (*):65633 (digit rank is 1)
Entrance Rank (*):52302
Currently on list? (*):no
Submitted:4/30/2015 22:51:14 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:119832
Status Flags:Verify
Score (*):36.406 (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 Repunit (archivable *)
Prime on list: no, rank 28
Subcategory: "Generalized Repunit"
(archival tag id 217999, tag last modified 2024-02-26 02:37:04)

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.

Serge Batalov writes (30 Apr 2015):  (report abuse)
Use these factors of N-1 for the plain N-1 test:
266155777
673598400099059
161928656890556401
161928657292960001
176061687120667147
225796030743689165059
788519439989193489376201081
Phi(8376,20060)/266155777
The latter is proven with Primo and the certificate is in FactorDB.org

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_id119832
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(20060^8377-1)/20059" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (20060^8377-1)/20059 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.19% and helper 0.03% (0.60% proof) (20060^8377-1)/20059 is Fermat and Lucas PRP! (95.3362s+0.0008s) [Elapsed time: 1.60 minutes]
modified2020-07-07 22:30:17
created2015-04-30 23:01:01
id165452

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
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