1829094416835 · 21290000 - 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:1829094416835 · 21290000 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (3,d=160128309135*2^1290001) [L3494]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3392 : Notte, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.95664266)
Rank (*):16139 (digit rank is 165)
Entrance Rank (*):2571
Currently on list? (*):no
Submitted:2/12/2015 11:57:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:119290
Status Flags:none
Score (*):43.7286 (normalized score 0.2897)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 20, weight 51.134722536938
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 218103, tag last modified 2023-03-11 16:02:30)

User comments about this prime (disclaimer):

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Serge Batalov writes (9 Oct 2015):  (report abuse)
Arithmetic progression (3,d=160128309135*2^1290001) [L3494]

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_id119290
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/llr.pl 1829094416835*2^1290000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 1829094416835*2^1290000-1 Using zero-padded AVX FFT length 128K, Pass1=128, Pass2=1K V1 = 9 ; Computing U0... V1 = 9 ; Computing U0...done.Starting Lucas-Lehmer loop... 1829094416835*2^1290000-1 is prime! (388341 decimal digits) Time : 776.987 sec. [Elapsed time: 12.95 minutes]
modified2020-07-07 22:30:17
created2015-02-12 12:11:51
id164896

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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