PrimeMind · Well Lab · Prime Wave → Zeta Lab

Prime Waves → Zeta Zeros

Start with the primes as standing waves. Each prime p gets one wave that completes p full cycles across a well, with equal energy. Add them up and watch the jagged prime composite bounce live.
Then press Morph to Zeta — and watch two things change simultaneously: the spacing shifts from linear to log, and the heights shift to 1+√n. The waves stretch, compress, and reorganise — until the combined wave is the Riemann zeta function on the ½ line, and its silences land exactly on the zeros.

individual prime waves
composite (sum of all)

Prime waves · linear spacing Zeta function · log spacing
26 prime waves · press Play to animate
0 zeros found in view · yellow dots = where the combined wave falls silent
2
Prime p=2
1 of 10 primes · composite building
Primes 10
Speed 1×
Stage 1 — Primes as standing waves. Wave p oscillates at frequency p — it completes exactly p full cycles across the well [0, 1]. Its height is 180/p (equal energy: 360 units shared over 2p peaks and troughs). The white composite is their sum. Notice: the composite looks noisy because the primes are irregularly spaced — they never form a clean pattern. That irregularity is precisely what makes them interesting.
Stage 2 — The morph. Two parameters shift simultaneously as the bar advances:
· Spacing: each wave's frequency changes from p (linear) to log(p) · t where t climbs with height — log spacing.
· Height: amplitude shifts from 180/p to 1 + √p.
Watch how the waves don't just fade — they physically reorganise, stretching and compressing as the two systems exchange. The composite loses its prime-well shape and develops a new character.
Stage 3 — The Riemann zeta function, live. With log spacing and height 1+√n, the combined wave is the Riemann–Siegel formula: Riemann's own zeta function ζ(½ + it) evaluated along the critical line. The yellow dots mark where the wave falls completely silent — every prime wave cancelling every other at the same instant. These are the Riemann zeta zeros. They've been computed to trillions of decimal places. Every single one sits exactly on the ½ line. Nobody knows why. That's the Riemann Hypothesis.