570409245 · 2143163 - 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:570409245 · 2143163 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:43106   (log10 is 43105.113455798)
Rank (*):57906 (digit rank is 4)
Entrance Rank (*):55477
Currently on list? (*):short
Submitted:6/17/2019 01:12:59 CDT
Last modified:6/17/2019 01:20:23 CDT
Database id:126557
Status Flags:TrialDiv
Score (*):36.9591 (normalized score 0.0006)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 13
Subcategory: "Sophie Germain (p)"
(archival tag id 220300, tag last modified 2020-05-17 15:50:28)

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_id126557
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"570409245*2^143163-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 570409245*2^143163-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 23, base 1+sqrt(23) Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 570409245*2^143163-1 is prime! (35.9147s+0.0003s) [Elapsed time: 36.00 seconds]
modified2020-07-07 17:30:13
created2019-06-17 01:13:01
id172242

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.