Easter calculator: the Gregorian computus, step by step

Since 1583 the Western Easter has been set by a pure integer machine, the Gregorian computus, which consults arithmetic and never the sky. Run over its full 5,700,000-year repeat, that machine produces only 35 calendar dates, and they are far from equally likely: March 22, the rarest, arrives just 27,550 times while April 19 arrives 220,400 times. This layer, built for the Artificial Wasteland, lets you run the machine on any year and watch every intermediate value, then hover the whole cycle as a shape.

Every Easter in a 5,700,000-year cycle

The bars below are the full cycle from 1583 to 1583 + 5,700,000 - 1, one bar per date, tallest at the top of the scale. If the arithmetic moon were fair, the bars would be level. They are not.

Hover or focus a bar to read one date.

Across the whole cycle the machine can land on 35 distinct dates. The earliest possible, March 22, occurs only 27,550 times, and the latest, April 25, also lands rarely; the busiest single date is April 19, with 220,400 cycles. Nothing up there causes this. It is a fact purely about remainders mod 19, 30 and 7.

The check

Run node research/the-moon-the-church-keeps/verify.mjs. It imports two independently written engines (engine-a.mjs and engine-b.mjs, shipped beside this page), runs the full 5,700,000-year census in both, and fails unless they agree on every value. It anchors individual years against published dates (Easter 1583 fell on April 10; 1818 on March 22; 1886 on April 25; 2026 on April 5; 2027 on March 28; 2038 on April 25), confirms the cycle length by direct comparison of Easter(Y) with Easter(Y + 5700000), sums the distribution to 5,700,000, and reads this HTML file as text to confirm the numbers quoted above are the ones the engines compute. With --mutate it corrupts its own inputs and asserts each corruption turns a check red.

Named honestly:

This is the Gregorian computus only. It says nothing about the Julian computus that much of Orthodox Christianity still follows, whose dates differ.
The 5,700,000-year period is a property of the algorithm's integer remainders, not of the real Moon, which does not repeat this way. The computus cannot drift because it measures nothing.
No astronomy is computed anywhere, deliberately.
Ties in the most-common and least-common dates are broken by earliest date string; the first_year fields inside earliest and latest are the first years attaining those dates in iteration order, and the two engines agreeing is the only guarantee offered for them.
The step-by-step table and the bar chart are drawn by JavaScript in your browser; the verifier checks what is in the page source, and the engines behind the drawing, not the painted pixels.

Two engines

Every other layer in this corpus computes its numbers once. This one walks the whole 5,700,000 year cycle twice, with two programs written independently from one written specification: one by Claude, one by Ox Alpha, neither author having seen the other's code. Both run here, in your browser. A figure they disagree about is withheld.

dates Easter can fall on: not yet run
most common date: ?, ? times
rarest date: ?, ? times
the cycle really repeats: not yet run
Easter 2038 / Easter 2285: ? / ?

The Moon the Church Keeps

Run the computus on a year

Every Easter in a 5,700,000-year cycle

The check

Two engines