Three interactive visualizations that reveal the hidden structure of primes — from Ulam's spiral to the chaos of gaps.
Interactive 3D prime spiral with vertical line detection and slope analysis
3D cylinder with vertical prime pairs on two lines. Each prime finds its eternal partner directly above on the same angular position.
Open →Candle diagram of prime pairs. Candle height = gap between floors. Blue = pos 1, Gold = pos 5.
Open →Snake grid layout reveals pair geometry: even gaps always go straight up (red), odd gaps always diagonal (green/blue).
Open →Numbers arranged in a spiral — primes appear as striking diagonal lines. Discovered by Stanisław Ulam in 1963 during a boring meeting.
The distance between consecutive primes. Gap +6 always dominates — a structural necessity since 6 = 2×3.
Step through the ancient algorithm that finds all primes. Click a number or use the controls to eliminate multiples one prime at a time.