4122429552750669 · 216567 - 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.

This prime's information:

Description:4122429552750669 · 216567 - 1
Verification status (*):Proven
Official Comment (*):Quadruplet (1)
Proof-code(s): (*):L4342 : Kaiser1, PolySieve, NewPGen, LLR
Decimal Digits:5003   (log10 is 5002.779091408)
Rank (*):91927 (digit rank is 7)
Entrance Rank (*):78740
Currently on list? (*):short
Submitted:3/8/2016 17:49:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:121383
Status Flags:none
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.
Quadruplet (archivable class *)
Prime on list: yes, rank 2
Subcategory: "Quadruplet (1)"
(archival tag id 218256, tag last modified 2023-03-11 15:53:59)

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 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/llr.pl 4122429552750669*2^16567-1 2>&1 Starting Lucas Lehmer Riesel prime test of 4122429552750669*2^16567-1 Using generic reduction AVX FFT length 1536 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop... 4122429552750669*2^16567-1 is prime! (5003 decimal digits) Time : 871.291 ms. [Elapsed time: 1.00 seconds]
modified2020-07-07 22:30:16
created2016-03-08 17:51:02

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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