The Riemann Hypothesis, explained (Jørgen Veisdal, 2016)
Present an argument or formula which (even barely) predicts what the next prime number will be (in any given sequence of numbers), and your name will be forever linked to one of the greatest achievements of the human mind, akin to Newton, Einstein and Gödel. (...)
Since the death of Riemann in 1866 at the modest age of 39, his groundbreaking paper has remained a landmark in the field of prime and analytic number theory. To this day Riemann’s hypothesis about the non-trivial zeros of the Riemann zeta function remains unsolved, despite extensive research by numerous great mathematicians for hundreds of years. Numerous new results and conjectures associated with the hypothesis are published each year, in the hope that one day a proof will be tangible.