Beefy Boxes and Bandwidth Generously Provided by pair Networks
Just another Perl shrine
 
PerlMonks  

Re^5: a close prime number

by Anonymous Monk
on Feb 12, 2005 at 20:51 UTC ( [id://430499]=note: print w/replies, xml ) Need Help??


in reply to Re^4: a close prime number
in thread a close prime number

My understanding was that they appeared with regular density
Regular density? Depending on what you mean by "regular" .. There is the famous prime number theorem. If π(n) is the number of primes less than n, then π(n) tends to n/ln(n) as n grows to infinity. Thus you could say that the density if primes within {1,..,n} is ln(n)/n. But this density gets smaller and smaller as n gets larger, thus the primes have to be getting (on average) farther and farther apart.

Also, as blazar mentions below. If you want to find a number X such that the first prime after X is at least X+200, just let X be 201! (that's with a factorial). Now X+1 may be prime, but X+2 is not prime since 2 divides X and 2. X+3 is not prime since 3 divides X and 3, etc... all the way until X+201.

Log In?
Username:
Password:

What's my password?
Create A New User
Domain Nodelet?
Node Status?
node history
Node Type: note [id://430499]
help
Chatterbox?
and the web crawler heard nothing...

How do I use this?Last hourOther CB clients
Other Users?
Others studying the Monastery: (8)
As of 2024-03-28 11:58 GMT
Sections?
Information?
Find Nodes?
Leftovers?
    Voting Booth?

    No recent polls found