1957 · 21284992 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:1957 · 21284992 + 1
Verification status (*):Proven
Official Comment:Divides GF(1284991,6)
Proof-code(s): (*):L3913 : Kadohara, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:386825   (log10 is 386824.42777908)
Rank (*):9371 (digit rank is 1)
Entrance Rank (*):3148
Currently on list? (*):short
Submitted:7/12/2014 19:25:40 CDT
Last modified:7/12/2014 23:50:04 CDT
Database id:118167
Status Flags:TrialDiv
Score (*):43.7166 (normalized score 0.8286)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 17, weight 51.2958221004941
Subcategory: "Divides GF(*,6)"
(archival tag id 217735, tag last modified 2016-03-15 13:57:15)

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.
machineXeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"1957*2^1284992+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 1957*2^1284992+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

1957*2^1284992+1 is prime! (636.3090s+0.0007s)
[Elapsed time: 10.60 minutes]
modified2014-12-15 15:47:32
created2014-07-12 19:41:04

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.