Prime counting function - Conservapedia

The Prime counting function counts the number of primes less than or equal to $\text{[math]}$ . The prime number theorem says that,

$\text{[math]}$ .

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

$\text{[math]}$ ,

where,

\text{[math]}

\text{[math]}

\text{[math]}

\text{[math]}

\text{[math]}

\text{[math]}

are the non-trivial zeros of the Riemann Zeta function.

Whilst the sum is over all $\text{[math]}$ it is needed only to add up to the term such that $\text{[math]}$ as after that $\text{[math]}$ .

The convergence of

\text{[math]}

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