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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.



These are the approximations:
Gauss (integral logarithm)
,
Legendre
,
and Riemann
.


"Approximations to the Distribution of Primes" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ApproximationsToTheDistributionOfPrimes/
Contributed by: Enrique Zeleny
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