1829094416835 · 21290000 - 1
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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: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 (*):9502 (digit rank is 165)
Entrance Rank (*):2571
Currently on list? (*):no
Submitted:2/12/2015 05:57:24 CDT
Last modified:10/10/2015 22:50:03 CDT
Database id:119290
Status Flags:TrialDiv
Score (*):43.7286 (normalized score 0.6466)

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 13, weight 51.1347225369376
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 218103, tag last modified 2017-02-02 09:20:09)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (9 Oct 2015): 
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.
machineUsing: Xeon 4c+4c 3.5GHz
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]
modified2015-04-20 07:32:09
created2015-02-12 06:11:51

Query times: 0.0004 seconds to select prime, 0.001 seconds to seek comments.