992 · 10312136 - 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:992 · 10312136 - 1
Verification status (*):Proven
Official Comment (*):Near-repdigit
Proof-code(s): (*):p356 : Rajala, Srsieve, NewPGen, OpenPFGW
Decimal Digits:312139   (log10 is 312138.99651167)
Rank (*):21946 (digit rank is 1)
Entrance Rank (*):3126
Currently on list? (*):no
Submitted:4/16/2013 17:54:36 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:113895
Status Flags:none
Score (*):43.0573 (normalized score 0.1424)

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.
Near-repdigit (archivable *)
Prime on list: no, rank 48
Subcategory: "Near-repdigit"
(archival tag id 217099, tag last modified 2024-02-07 04:37:20)

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_id113895
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 992 10 312136 -1 2>&1 [Elapsed time: 9.196 seconds]
modified2020-07-07 22:30:19
created2013-04-16 18:05:02
id158149

fieldvalue
prime_id113895
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"992*10^312136-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 992*10^312136-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 69.90% 992*10^312136-1 is prime! (10611.6368s+0.0142s) [Elapsed time: 2.95 hours]
modified2020-07-07 22:30:19
created2013-04-16 18:08:01
id158150

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