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The '''Prime Number Theorem''' is one of the most famous theorems in mathematics.  It states that the number of primes not exceeding n is asymptotic to <math>\frac{n}{\log(n)}</math>, where log(n) is the logarithm of (n) to the base e.   

The '''Prime Number Theorem''' is one of the most famous theorems in mathematics.  It states that the number of primes not exceeding n is asymptotic to <math>\frac{n}{\log(n)}</math>, where log(n) is the logarithm of (n) to the base e.   

The number of primes not exceeding n is commonly written as <math>\pi(n)</math>, and an asymptotic relationship between a(n) and b(n) is commonly designated as a(n)~b(n).  (This does not mean that a(n)-b(n) is small as n increases.  It means the ratio of a(n) to b(n) approaches one as n increases.)

The number of primes not exceeding n is commonly written as <math>\pi(n)</math> the [[Prime counting function]], and an asymptotic relationship between a(n) and b(n) is commonly designated as a(n)~b(n).  (This does not mean that a(n)-b(n) is small as n increases.  It means the ratio of a(n) to b(n) approaches one as n increases.)

The Prime Number Theorem thus states that <math> \pi(n) </math>~<math> n/ \log(n)</math> .

The Prime Number Theorem thus states that <math> \pi(n) </math>~<math> n/ \log(n)</math> .