Prime Tread Wheel

The number line rolls up onto a wheel, one layer per pass. Layer n brings n evenly spaced ticks. A tick that lands on a line an older layer already made adds nothing. A layer whose ticks all make new lines is prime, and its ring stays gold.

The number line rolls up onto the wheel, one layer per pass. Layer n brings n evenly spaced ticks. A tick that lands on a line an older layer made adds nothing; a layer whose ticks all make new lines is prime, and its ring stays gold.

Wheel

Circumference

A fixed circle never grows, so number x lands x ÷ circumference of the way round, turn after turn.

The drum never grows, so layer m squeezes its m numbers into one turn: the unit shrinks to 1/m of a turn instead of the wheel growing. A fraction of a turn is the same spot on every band, so the growing wheel's lines stand straight up the drum as columns. Look closer to slit it at the seam and lay it flat.

Speed 1×

Roll to layer

Sound: each prime rings as it lands, pitched by where round the wheel it lands, so repeating arms become repeating notes

Numbers

Use

Sieve

Quick looks

Look

These change every wheel, rolling or up close, and the ledger. The page keeps them.

Color Wheel p Ticks Line color

Ticks Lines Layer tracks Older lines brighter

Tick size Line brightness Layer brightness Old marks longer

Layer groups

Every layer follows the first group it fits, top to bottom. Untick a group to hide its layers, click a swatch to recolor it (that also sets the color to these groups), and use the arrows to change which group wins.

Dim ticks on older lines

Close look

Holds the wheel still. Scroll or pinch to zoom, drag to move, tap a tick to read it and light up its line.

Layers

Layout Spacing Spotlight

Turn

Numbers up close Collatz trail for the tapped number

Last layer

Charts

The numbers behind this chart

Ledger

One row per layer, ticks left to right, so row n holds the n numbers that layer rolled up: 1, then 2 3, then 4 5 6, and so on. Cells take the Look's colors, and cells the Numbers or the groups hide stay dark. In New-or-older colors, prime rows are gold all the way across, and the blue cells line up in straight streaks pointing back to the top corner: each streak is one older line, landed on again and again. Once the layers outnumber the pixels, each pixel blends the cells under it.

Show one cell per pixel instead. The skipped cells fall in a rhythm that beats against the small wheels and draws big squares that change with zoom.

Lens

Point at the ledger, or tap it, to move the lens. With the ledger focused, the arrow keys move it too.

Ball trough

Your sieve with balls: pour n balls into a trough one unit long, then widen it a column at a time. A flat top row means that width fits n evenly, so n isn't prime. Past the point where the pile is as wide as it is tall, every pile is an earlier one on its side.

Balls

More wheels

Collatz on a doubling wheel, Riemann's zeros as spinning wheels, Goldbach on a folded wheel, twin primes as gear seats, and prime races: Problem Wheels. The same counting wrapped onto a sphere: Geometric Math Globe.

Prime layers so far

Shown on the last layer