Wolfram Demonstrations Project

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.

These are the approximations:

Gauss (integral logarithm)

Legendre

and Riemann

Contributed by: Enrique Zeleny

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Approximations to the Distribution of Primes