Crate const_primes

Generate and work with prime numbers in const contexts.

This crate lets you for example pre-compute prime numbers at compile time, store them in the binary, and use them later for related computations, or check whether a number is prime in a const function.

no_std compatible when the serde feature is disabled.

This version of the crate supports Rust versions 1.81.0 and up, while versions 0.8.7 and older support Rust versions 1.67.1 and up.

Example: generate primes at compile time and use them later for related computations

The struct Primes is a wrapper around an array of primes generated by a segmented sieve of Eratosthenes and can be used as a cache of prime numbers for related computations:

// The first 100 primes
const CACHE: Primes<100> = Primes::new();

// Primality testing
const CHECK_42: Option<bool> = CACHE.is_prime(42);
const CHECK_541: Option<bool> = CACHE.is_prime(541);
assert_eq!(CHECK_42, Some(false));
assert_eq!(CHECK_541, Some(true));

// Prime counting
const PRIMES_LEQ_100: Option<usize> = CACHE.prime_pi(100);
assert_eq!(PRIMES_LEQ_100, Some(25));

// Prime factorization
assert_eq!(CACHE.prime_factorization(3072).collect::<Vec<_>>(), &[(2, 10), (3, 1)]);
// and more!

// If questions are asked about numbers outside the cache it returns None
assert!(CACHE.is_prime(1000).is_none());
assert!(CACHE.prime_pi(1000).is_none());

Example: primality checking

Use is_prime to test whether a given number is prime:

use const_primes::is_prime;

const CHECK: bool = is_prime(18_446_744_073_709_551_557);

assert!(CHECK);

Example: generate the three primes after 5000000031

The crate also provides prime generation and sieving functionality for computing arrays of large prime numbers above or below some limit, without having to also include every single prime number from 2 and up in the resulting constant, and thus potentially the binary.
This functionality is most conveniently accessed through the macros primes_segment! and sieve_segment! that automatically compute the size of the prime sieve that is needed for a certain computation.

Compute the three primes greater than or equal to 5000000031:

use const_primes::{primes_segment, GenerationError};

const N: usize = 3;
const PRIMES_GEQ: Result<[u64; N], GenerationError> = primes_segment!(N; >= 5_000_000_031);

assert_eq!(PRIMES_GEQ, Ok([5_000_000_039, 5_000_000_059, 5_000_000_063]));

Example: find the next or previous prime numbers

Find the next or previous prime numbers with next_prime and previous_prime if they exist:

use const_primes::{previous_prime, next_prime};

const NEXT: Option<u64> = next_prime(25);
const PREV: Option<u64> = previous_prime(25);
const NO_SUCH: Option<u64> = previous_prime(2);
const TOO_BIG: Option<u64> = next_prime(u64::MAX);

assert_eq!(NEXT, Some(29));
assert_eq!(PREV, Some(23));
assert_eq!(NO_SUCH, None);
assert_eq!(TOO_BIG, None);

and more!

Features

fast_test: Significantly speed up the is_prime function by depending on the machine_prime crate. Raises the MSRV to 1.84.0.

serde: derives the Serialize and Deserialize traits from the serde crate for the Primes struct, as well as a few others. Uses the serde_arrays crate to do this, and that crate uses the standard library.

zerocopy: derives the IntoBytes trait from the zerocopy crate for the Primes struct.

rkyv: derives the Serialize, Deserialize, and Archive traits from the rkyv crate for the Primes struct.

Re-exports

pub use cache::Primes;

Modules

cache

This module contains the implementation of the type Primes (and related iterators), which functions as a cache of prime numbers for related computations.

Macros

primes_segment

Generate arrays of large prime numbers without having to store all primes from 2 and up in the result, and thus potentially the binary.

sieve_segment

Generate arrays of the prime status of large numbers without having to store the prime status of every single integer smaller than the target in the result, and thus potentially the binary.

Enums

GenerationError

The error returned by primes_lt and primes_geq if the input is invalid or does not work to produce the requested primes.

SieveError

The error returned by sieve_lt and sieve_geq if the input is invalid or does not work to sieve the requested range.

Functions

is_prime

Returns whether n is prime.

isqrt

Returns the largest integer smaller than or equal to √n.

next_prime

Returns the smallest prime greater than n if there is one that can be represented by a u64.

previous_prime

Returns the largest prime smaller than n if there is one.

prime_pi

Returns an array of size N where the value at a given index is how many primes are less than or equal to the index.

primes

Returns the N first prime numbers.

primes_geq

Returns the N smallest primes greater than or equal to lower_limit.

primes_lt

Returns the N largest primes less than upper_limit.

sieve

Returns an array of size N where the value at a given index indicates whether the index is prime.

sieve_geq

Returns an array of size N that indicates which of the N smallest integers greater than or equal to lower_limit are prime.

sieve_lt

Returns an array of size N that indicates which of the N largest integers smaller than upper_limit are prime.