(4073416111 - 1)/40733

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:(4073416111 - 1)/40733
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:74267   (log10 is 74266.408232087)
Rank (*):54677 (digit rank is 1)
Entrance Rank (*):40903
Currently on list? (*):short
Submitted:3/9/2015 05:59:43 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:119521
Status Flags:Verify
Score (*):38.6373 (normalized score 0.0016)

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 4
Subcategory: "Generalized Repunit"
(archival tag id 217915, 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 (9 Mar 2015):  (report abuse)
CHG proof at 27.46% available at:
This proof relies on an ECPP proof of a 19632-digit helper prime that divides N-1.

At time of discovery, this prime set the record for the largest Generalized Repunit prime, as well as the largest NTG (non-trivial gigantic) prime.

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(40734^16111-1)/40733" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (40734^16111-1)/40733 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.14% and helper 0.00% (0.42% proof) (40734^16111-1)/40733 is Fermat and Lucas PRP! (600.1030s+0.0017s) [Elapsed time: 10.00 minutes]
modified2020-07-07 22:30:17
created2015-03-09 06:01:01

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