Module primes 

Prime number distribution, sieves, and rendering utilities.

Structs

PrimeDistributionRenderer

Maps primes to glyph positions, sizes, and colors for engine rendering.

PrimeGlyph

A renderable glyph descriptor for a prime.

SacksSpiral

Sacks spiral: polar plot where integer n is at angle sqrt(n) * 2*pi, radius sqrt(n).

UlamSpiral

Ulam spiral: maps positive integers to a 2D grid position via a spiral walk, highlighting prime positions.

Functions

is_prime

Primality test. Uses trial division for small n, Miller-Rabin for large n.

nth_prime

Returns the n-th prime (1-indexed: nth_prime(1) == 2).

prime_counting

Prime counting function pi(x): number of primes <= x.

prime_factorization

Prime factorization of n, returned as sorted (prime, exponent) pairs.

prime_gaps

Gaps between consecutive primes up to limit.

sieve_of_eratosthenes

Classic sieve of Eratosthenes returning all primes up to limit.

twin_primes

Twin prime pairs (p, p+2) up to limit.