Prime Sieve Constant

A binary sieve made from centered pyramid terms. Each reciprocal row becomes a periodic mask; OR the rows to mark composite positions, then invert the result to reveal the prime indicator.

Centered binary terms

Reciprocal masks and sieve result

reciprocal hit composite slot prime slot bit 1 sentinel

Pyramid valueThe nth row is n ones followed by n zeros, so its value is 2^n(2^n - 1).

Mask behaviorFor row n, the recurring 1s land on 2n, 3n, 4n..., which is exactly the composite-marking rhythm for that stride.

Prime constantThe OR row marks every visible composite. The NOT row leaves 1s at primes, with bit 1 treated separately as a sentinel.