4122429552750669 · 216567 + 5
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help)value
Description:4122429552750669 · 216567 + 5
Verification status (*):PRP
Official Comment:Quadruplet (3), ECPP
Proof-code(s): (*):c83 : Kaiser1, PolySieve, NewPGen, Primo
Decimal Digits:5003   (log10 is 5002.779091408)
Rank (*):81151 (digit rank is 5)
Entrance Rank (*):78740
Currently on list? (*):short
Submitted:3/8/2016 11:50:51 CDT
Last modified:3/8/2016 12:20:35 CDT
Database id:121385
Status Flags:Verify, TrialDiv
Score (*):30.2909 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 389
Subcategory: "ECPP"
(archival tag id 218253, tag last modified 2017-10-19 05:50:25)
Quadruplet (archivable class *)
Prime on list: yes, rank 1
Subcategory: "Quadruplet (3)"
(archival tag id 218254, tag last modified 2016-03-08 12:20:38)

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_id121385
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"4122429552750669*2^16567+5" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 4122429552750669*2^16567+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 0.19% and helper 0.13% (0.70% proof)


4122429552750669*2^16567+5 is Fermat and Lucas PRP! (2.5438s+0.0839s)
[Elapsed time: 3.00 seconds]
modified2016-04-08 12:40:26
created2016-03-08 11:51:04
id167019

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.