193 · 23329782 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or π(x) for x up to 100,000,000,000,000,000.

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:193 · 23329782 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(3329780)
Proof-code(s): (*):L3460 : Ottusch, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1002367   (log10 is 1002366.54657931)
Rank (*):185 (digit rank is 1)
Entrance Rank (*):98
Currently on list? (*):short
Submitted:7/25/2014 17:58:37 CDT
Last modified:7/25/2014 20:20:04 CDT
Database id:118254
Status Flags:TrialDiv
Score (*):46.6402 (normalized score 18.3863)

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.
Fermat Divisors (archivable *)
Prime on list: yes, rank 1, weight 51.9029809315416
Subcategory: "Divides Fermat"
(archival tag id 217768, tag last modified 2016-03-15 13:57:14)

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_id118254
person_id9
machineXeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"193*2^3329782+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 193*2^3329782+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


193*2^3329782+1 is prime! (4842.2594s+0.0013s)
[Elapsed time: 80.70 minutes]
modified2014-12-15 15:47:32
created2014-07-25 18:01:01
id163820

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.