62399583639 · 9923# - 3399421517

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:62399583639 · 9923# - 3399421517
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (4,d=30), ECPP
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:4285   (log10 is 4284.5831323473)
Rank (*):89423 (digit rank is 3)
Entrance Rank (*):88270
Currently on list? (*):short
Submitted:11/2/2021 18:13:37 CDT
Last modified:11/2/2021 18:37:41 CDT
Database id:132893
Status Flags:Verify, TrialDiv
Score (*):29.8092 (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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 1
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 226416, tag last modified 2021-11-02 18:37:44)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 177, weight 39.376875942436
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 226417, tag last modified 2022-05-27 13:58:11)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 543
Subcategory: "ECPP"
(archival tag id 226418, tag last modified 2022-07-03 06:37:26)

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"62399583639*9923#-3399421517" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 62399583639*9923#-3399421517 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N-1 BLS with factored part 0.32% and helper 0.01% (0.99% proof)

62399583639*9923#-3399421517 is Fermat and Lucas PRP! (1.3573s+0.0002s)
[Elapsed time: 1.00 seconds]
modified2021-11-02 18:16:08
created2021-11-02 18:16:07

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.