(42157323 + 1)2 - 2

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:(42157323 + 1)2 - 2
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p424 : Liiv, Cksieve, OpenPFGW
Decimal Digits:510749   (log10 is 510748.89622654)
Rank (*):4333 (digit rank is 1)
Entrance Rank (*):4286
Currently on list? (*):yes
Submitted:9/30/2021 11:10:36 CDT
Last modified:10/1/2021 04:37:15 CDT
Database id:132772
Status Flags:TrialDiv
Score (*):44.5704 (normalized score 1.1332)

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(42^157323+1)^2-2" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing (42^157323+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 3+sqrt(17)
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)

(42^157323+1)^2-2 is prime! (60633.8965s+0.0053s)
[Elapsed time: 16.84 hours]
modified2021-10-01 04:01:35
created2021-09-30 11:11:01

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.