I will start this blog the way Bernhard Riemann started his paper: with Euler's product formula that John Derbyshire called the golden key:
This holds for any complex number with . If you look up a proof in any modern textbook, you will find a number technical rearrangements that end up in an examination of the absolute convergence on both sides. But actually, the formula is nothing but a fancy way of writing out the Sieve of Eratosthenes. Let's start by writing out the sum on the left hand side: Continue reading In the Beginning, There Was... Euler's Formula!