Home▸Mathematics▸Analytic Number Theory: Prime Spiral & the Prime-Counting Function

🔢 Analytic Number Theory: Prime Spiral & the Prime-Counting Function

Watch integers rise as a 3D Sacks spiral while prime numbers light up. Sweep the range, animate the build-up, isolate primes only, and compare the live prime count pi(N) against the Prime Number Theorem estimate N / ln(N) in real time.

Mathematics3DModerate60 FPS

Details

CategoryMathematics

RenderingThree.js · WebGL

DifficultyModerate

Target FPS60

ControlsRange slider (200-20000) sets how many integers N are plotted on the spiral; build-up speed slider (200-6000 points/sec) controls how fast new points animate in when N changes; 'Primes only' button hides every composite instance, leaving just the prime arms of the spiral visible; 'Auto-rotate' button toggles a slow orbit of the camera around the growing spiral.

Three.jsnumber theoryprime numbersRiemann zeta functionInstancedMesh

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⚙ Under the hood

Watch a rising Sacks-style spiral of the integers light up with prime numbers. Sweep the range up to 20,000, animate the build-up, isolate primes only, and compare the live prime count pi(N) against the Prime Number Theorem estimate N / ln(N) in real time.

Three.jsnumber theoryprime numbersRiemann zeta functionInstancedMesh

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install