Approximating the Riemann Zeta Function with Coprime n-tuples

At the age of twenty-eight, Leonhard Euler, now one of the greatest mathematicians of all time, gained immediate fame after solving the Basel problem. For over eighty years this problem had withstood the attempts of leading mathematicians until it was finally solved by Euler in 1734. Euler generalized the problem and over a century later Bernhard Riemann defined his zeta function, extending the problem to complex numbers. Riemann’s zeta function has since become the head of the most important unsolved problem in pure mathematics, the Riemann hypothesis.