The Riemann hypothesis was already known to be equivalent to a not-very-complicated statement about the distribution of primes. Let Ï€ be the number of primes less than n. Then the Riemann hypothesis is equivalent to:
for all Îµ > 0. This fact, which goes back at least to Riemann, is the main reason why the Riemann hypothesis is of interest. In 2002, Jeffrey Lagarias found an even more elementary statement.:
where Hn is the nth Harmonic number (the sum of reciprocals less than or equal to n). It almost looks you could solve it, doesn’t it?