(3828411491 - 1)/38283

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:(3828411491 - 1)/38283
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH2 : Wu_T, OpenPFGW, Primo, CHG
Decimal Digits:52659   (log10 is 52658.868875181)
Rank (*):60337 (digit rank is 1)
Entrance Rank (*):40468
Currently on list? (*):short
Submitted:2/10/2013 19:40:20 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:111177
Status Flags:Verify
Score (*):37.5769 (normalized score 0.0005)

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: yes, rank 16
Subcategory: "Generalized Repunit"
(archival tag id 215070, 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.

Tom Wu writes (11 Sep 2014):  (report abuse)
CHG proof with 27.15% of N-1 factored. This proof also relies on a 13956-digit helper prime proven with ECPP.

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"(38284^11491-1)/38283" 2>&1 PFGW Version [GWNUM 26.5] (38284^11491-1)/38283 1/1 mro=0 trial factoring to 17165048 (38284^11491-1)/38283 has no small factor. [Elapsed time: 73.492 seconds]
modified2020-07-07 22:30:23
created2013-02-10 19:48:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"(38284^11491-1)/38283" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (38284^11491-1)/38283 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 29 Running N+1 test using discriminant 47, base 1+sqrt(47) Calling N-1 BLS with factored part 0.12% and helper 0.01% (0.37% proof) (38284^11491-1)/38283 is Fermat and Lucas PRP! (1537.6362s+0.0022s) [Elapsed time: 25.63 minutes]
modified2020-07-07 22:30:23
created2013-02-10 19:53:01

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