Practical Computations of the Mertens Function: $M(10^{24})$ and $M(10^{25})$

Greg Hurst

The Mertens function is defined as $M(x)={\sum }_{n\le x}\hat{I}¼(n)$, where $\hat{I}¼(n)$ is the Möbius function. This paper describes a practical implementation of the classical $O(x^{2/3+\va…