Build intuition early

Every number has a shape. Primes are towers.

Build any number out of cubes and let it fold into its most compact form — its prime shape. Primes stay stubborn towers. Composites fold into plates, bricks, and cubes. Suddenly factors, volume, and surface area are things you can stack, spin, and see.

Launch the explorer See how it works

+Surface

Minimize exposed faces while keeping volume fixed.

+Spatial

Rotate, zoom, and compare shapes in 3D to build intuition.

+Math talk

Connect factors, primes, and efficiency to real geometry.

Why prime shapes?

Math that you can stack, spin, and see.

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Surface area efficiency. Prime shapes expose the fewest faces, showing students the cost of stretched dimensions.
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Factor sense. Each dimension is a factor of N. Students see why certain triples pack tighter.
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Cube-first visuals. N is literal: one cube = one unit. No abstractions required.

Grades 3–8 STEM clubs Math circles

the shape family tree

Every number in the universe is one of these shapes.

Count a number's prime factors and you know its silhouette. That's the whole system — and it never breaks.

1 prime factor

Towers

7 = 1×1×7. Primes are so stubborn they only make a tower — you can see primality.

2 prime factors

Plates

6 = 1×2×3. Two primes make a flat slab — one layer thick, every time.

3 prime factors

Pure bricks

30 = 2×3×5. Three primes, three dimensions — every edge is a prime number.

4+ prime factors

Fused bricks

210 = 5×6×7. Four primes won't fit in three dimensions — two of them must fuse.

Why can't two dimensions fuse at once? That's a theorem — and a fun one. Dig into the math →

fresh from the lab

Discoveries hiding in plain sight.

We computed the prime shape of every number up to 200,000. The blocks had surprises waiting.

The number that lies

5×8×9 · SA 314

6×6×10 · SA 312

360 breaks intuition. The cube-like 5×8×9 loses to 6×6×10. "Closest to cube" and "least surface" aren't the same thing — only 65 numbers below 50,000 expose the difference.

An open problem

200,000 checked

No ties. Ever. In every number we've tested, exactly one shape wins the surface-area race. Nobody has proven it must be unique. Find a tie — or prove none exists — and you've done real mathematics.

The great reshuffle

216 = 6×6×6

720 = 8×9×10

Numbers reorganize. Double 216's perfect cube and every dimension changes. And 720 folds into 8×9×10 — three consecutive numbers. The primes re-deal themselves for maximum balance.

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