69285767989 · 5303# + 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:69285767989 · 5303# + 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (8,d=3026809034*5303#)
Proof-code(s): (*):p406 : DavisK, Luhn, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW
Decimal Digits:2271   (log10 is 2270.1563430235)
Rank (*):95137 (digit rank is 1892)
Entrance Rank (*):92070
Currently on list? (*):short
Submitted:8/11/2019 02:19:28 CDT
Last modified:8/11/2019 02:50:11 CDT
Database id:126732
Status Flags:TrialDiv
Score (*):27.8321 (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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 1, weight 52.8424063518097
Subcategory: "Arithmetic progression (8,d=*)"
(archival tag id 220377, tag last modified 2019-08-11 02:50:13)

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_id126732
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"69285767989*5303#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 69285767989*5303#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.34% 69285767989*5303#+1 is prime! (0.8596s+0.0008s) [Elapsed time: 1.00 seconds]
modified2020-07-07 17:30:13
created2019-08-11 02:21:02
id172410

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.