9813
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Approximations to the Distribution of Primes
The function
, the prime-counting function, gives the number of primes less than or equal to
. The plots shown are of the differences between
and the approximations to
due to Gauss, Legendre, and Riemann.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Automatic Animation
SNAPSHOTS
DETAILS
These are the approximations:
Gauss (integral logarithm)
,
Legendre
,
and Riemann
.
RELATED LINKS
Prime Number Theorem
(
Wolfram
MathWorld
)
Prime Counting Function
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Approximations to the Distribution of Primes
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ApproximationsToTheDistributionOfPrimes/
Contributed by:
Enrique Zeleny
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Prime Plaid
Enrique Zeleny V.
Why a Number Is Prime
Enrique Zeleny
Cycles in Sums of Prime Factors
Enrique Zeleny
Sieve of Eratosthenes
George Beck
Distribution of Primes
Hector Zenil
How the Primes Are Distributed
Bill Collins
Distribution of the Last Digit of the Primes
Soumyajit Mandal
How the Zeros of the Zeta Function Predict the Distribution of Primes
Robert Baillie
Gaussian Primes
Stephen Wolfram
Palindrome Primes
Peter Bohus and Márton Károlyi
Related Topics
Number Theory
Prime Numbers
Recreational Mathematics
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+