Sieve of Eratosthenes · branch-form analysis
Runs the Sieve-N procedure from scirealm.org/PrimeSieve.html: at each stage it
derives the mathematical form of the surviving branches, solves the modulus condition for the next prime,
and colours every integer by what the sieve has actually established about it.
Method: John B. Wilson — scirealm.org/PrimeSieve.html. All values computed live in this page; nothing is tabulated in advance.
Each tick is one residue in a single repeat distance. Filled ticks survive the sieve; the gaps are the multiples struck out. This is the pattern that repeats forever — the wheel every fast sieve implementation turns.
Step the sieve:
Sieve-23 is the ceiling. Rendering Sieve-P needs the previous level’s branch list as parents: Sieve-23 consumes Sieve-19’s 1,658,880 residues (13 MB), while Sieve-29 would need 36,495,360 (279 MB). Primorials stay exact JS integers to Sieve-41 (3.0×1014); the a2≡1 test is built by CRT rather than by squaring residues, so it never loses precision.