109766820328 · 7877# - 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.

Description:109766820328 · 7877# - 1
Verification status (*):Proven
Official Comment (*):Cunningham chain (8p+7)
Proof-code(s): (*):p395 : Angel, Augustin, NewPGen, OpenPFGW
Decimal Digits:3385   (log10 is 3384.3845771172)
Rank (*):90337 (digit rank is 14)
Entrance Rank (*):83316
Currently on list? (*):short
Submitted:10/31/2016 21:59:24 CDT
Last modified:10/31/2016 22:20:29 CDT
Database id:122450
Status Flags:TrialDiv
Score (*):29.0757 (normalized score 0)

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.
Cunningham Chains (1st kind) (archivable class *)
Prime on list: yes, rank 1, weight 45.28660106269
Subcategory: "Cunningham chain (8p+7)"
(archival tag id 218494, tag last modified 2016-10-31 22:20:33)

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 -tp -q"109766820328*7877#-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 109766820328*7877#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7883, base 1+sqrt(7883) Calling Brillhart-Lehmer-Selfridge with factored part 33.37% 109766820328*7877#-1 is prime! (3.6284s+0.0014s) [Elapsed time: 4.00 seconds]
modified2020-07-07 17:30:16
created2016-10-31 22:01:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.