Prime counting function

From Conservapedia
Jump to: navigation, search

The Prime counting function counts the number of primes less than or equal to . The prime number theorem says that,

.

In 1859 Bernhard Riemann presented a paper On the number of primes less than a given number he showed this to be exactly,

,

where,

is Möbius Mu function,
is the natural logarithm of
are the non-trivial zeros of the Riemann Zeta function.

Whilst the sum is over all it is needed only to add up to the term such that as after that .

The convergence of

is dependent on the Riemann hypothesis and if true is better behaved.