1 · Walk the staircase

The prime count climbing, against the smooth curve Gauss guessed at fifteen.

Try this. Stretch the range and watch the two curves. The staircase never strays far from the smooth guess, and never quite agrees with it either. The gap between them is the wobble the zeros orchestrate.

The smooth curve is Gauss's logarithmic-integral guess, computed here by direct integration. In this whole range the truth runs slightly under the guess; Littlewood proved the sign nevertheless flips infinitely often, unimaginably far out.