682156 · 79682156 + 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:682156 · 79682156 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4472 : Harvanek, Gcwsieve, MultiSieve, PrimeGrid, LLR
Decimal Digits:1294484   (log10 is 1294483.53997)
Rank (*):741 (digit rank is 1)
Entrance Rank (*):83
Currently on list? (*):yes
Submitted:10/9/2016 16:35:56 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:122349
Status Flags:none
Score (*):47.4248 (normalized score 9.7719)

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 Cullen (archivable *)
Prime on list: yes, rank 17
Subcategory: "Generalized Cullen"
(archival tag id 218446, tag last modified 2024-08-17 05:37:11)

User comments about this prime (disclaimer):

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PrimeGrid writes (27 Nov 2016):  (report abuse)
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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_id122349
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"682156*79^682156+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 682156*79^682156+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 682156*79^682156+1 is prime! (15695.4245s+0.0457s) [Elapsed time: 4.36 hours]
modified2020-07-07 22:30:16
created2016-10-09 16:41:01
id167989

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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