  Bertrand's Postulate ensures existence of prime $p$ between $n$ and $2n$, $n$
an integer $\geq 2$ and the sieve of Eratosthenes, a very simple ancient
algorithm, generates all prime numbers up to any given limit. Combining the
above two, in this paper, we provide a simple fast moving algorithm to generate
prime numbers up to any given limit. We also discuss Riemann zeta function
related to generating of prime numbers.
