163 · 21129934 + 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:163 · 21129934 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(1129933,10)
Proof-code(s): (*):L1751 : Eckhard, Srsieve, PrimeGrid, LLR
Decimal Digits:340147   (log10 is 340146.23930819)
Rank (*):16484 (digit rank is 1)
Entrance Rank (*):315
Currently on list? (*):short
Submitted:12/26/2010 05:04:17 CDT
Last modified:12/26/2010 13:50:03 CDT
Database id:97112
Status Flags:none
Score (*):43.3214 (normalized score 0.2801)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 17, weight 48.415187496571
Subcategory: "Divides GF(*,10)"
(archival tag id 213037, tag last modified 2021-02-18 04:50:24)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 163 2 1129934 1 2>&1 [Elapsed time: 10.301 seconds]
modified2020-07-07 17:30:32
created2010-12-26 05:05:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"163*2^1129934+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 163*2^1129934+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 163*2^1129934+1 is prime! (1858.1823s+0.0277s) [Elapsed time: 30.97 minutes]
modified2020-07-07 17:30:32
created2010-12-26 05:12:07

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.