4111286921397 · 266420 + 5

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:4111286921397 · 266420 + 5
Verification status (*):PRP
Official Comment (*):Triplet (3)
Proof-code(s): (*):c88 : Kaiser1, PolySieve, Primo
Decimal Digits:20008   (log10 is 20007.026289788)
Rank (*):66988 (digit rank is 6)
Entrance Rank (*):65184
Currently on list? (*):short
Submitted:4/23/2019 14:01:55 CDT
Last modified:4/23/2019 14:20:11 CDT
Database id:126415
Status Flags:Verify, TrialDiv
Score (*):34.5873 (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.
Triplet (archivable class *)
Prime on list: yes, rank 1
Subcategory: "Triplet (3)"
(archival tag id 220236, tag last modified 2019-04-23 14:20:12)

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_id126415
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"4111286921397*2^66420+5" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 4111286921397*2^66420+5 [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 0.09% and helper 0.01% (0.28% proof) 4111286921397*2^66420+5 is Fermat and Lucas PRP! (12.2652s+0.0003s) [Elapsed time: 13.00 seconds]
modified2020-07-07 17:30:13
created2019-04-23 14:13:01
id172097

Query times: 0.0001 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.