1993191 · 23986382 - 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:1993191 · 23986382 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3532 : Batalov, Gcwsieve, LLR
Decimal Digits:1200027   (log10 is 1200026.8557239)
Rank (*):708 (digit rank is 1)
Entrance Rank (*):71
Currently on list? (*):short
Submitted:5/1/2015 16:42:51 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:119835
Status Flags:none
Score (*):47.1924 (normalized score 9.2546)

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.
Generalized Woodall (archivable *)
Prime on list: yes, rank 13
Subcategory: "Generalized Woodall"
(archival tag id 218000, tag last modified 2024-02-26 15:37:18)

User comments about this prime (disclaimer):

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Serge Batalov writes (1 May 2015):  (report abuse)
1993191 · 41993191 - 1

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_id119835
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/llr.pl 1993191*2^3986382-1 2>&1 Starting Lucas Lehmer Riesel prime test of 1993191*2^3986382-1 Using zero-padded AVX FFT length 400K, Pass1=320, Pass2=1280 V1 = 3 ; Computing U0... V1 = 3 ; Computing U0...done.Starting Lucas-Lehmer loop... 1993191*2^3986382-1 is prime! (1200027 decimal digits) Time : 8323.199 sec. [Elapsed time: 2.31 hours]
modified2020-07-07 22:30:17
created2015-05-01 16:51:01
id165455

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