1938662032575 · 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:1938662032575 · 21290000 - 1
Verification status (*):Proven
Official Comment:Arithmetic progression (1,d=10032831585*2^1290001) [p199]
Proof-code(s): (*):L927 : Brown1, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.98190864)
Rank (*):9530 (digit rank is 70)
Entrance Rank (*):2774
Currently on list? (*):short
Submitted:4/1/2015 10:59:51 CDT
Last modified:10/1/2015 20:20:03 CDT
Database id:119668
Status Flags:TrialDiv
Score (*):43.7286 (normalized score 0.6355)

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: yes, rank 2
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 218089, tag last modified 2016-12-25 17:20:03)

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 1938662032575*2^1290000-1 2>&1
Starting Lucas Lehmer Riesel prime test of 1938662032575*2^1290000-1
Using zero-padded AVX FFT length 128K, Pass1=128, Pass2=1K
V1 = 5 ; Computing U0...
V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop...

1938662032575*2^1290000-1 is prime! (388341 decimal digits) Time : 777.297 sec.
[Elapsed time: 12.97 minutes]
modified2015-04-20 07:32:09
created2015-04-01 11:01:01

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