Primes from zeros

The white staircase is ψ(x), which climbs by ln p at every prime power pᵏ. The gold curve starts out smooth, and each pair of zeros 1/2 ± iγ takes away one wave, faster the higher the zero. Add pairs: with a few the curve only sways round the steps, by ten or so it begins to follow the bigger ones, and with hundreds the flats and jumps are clear, with a little overshoot at each jump and, exactly at a jump, the value halfway between the two levels. Click on the graph to compare ψ at that point with what the zeros give.