const-primes

A crate for generating and working with prime numbers in const contexts.

#![no_std] compatible.

Examples

Generate arrays of prime numbers with the function primes which uses a segmented sieve of Eratosthenes.

const PRIMES: [u32; 10] = primes();
assert_eq!(PRIMES[5], 13);
assert_eq!(PRIMES, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]);

or with the type Primes which ensures that a non-zero number of primes are generated:

const PRIMES: Primes<10> = Primes::new();
assert_eq!(PRIMES[5], 13);
assert_eq!(PRIMES, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]);

It also lets you reuse it as a cache of primes for related computations:

const CACHE: Primes<100> = Primes::new();

// For 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));

// Or for prime counting
const PRIMES_LEQ_100: Option<usize> = CACHE.count_primes_leq(100);
assert_eq!(PRIMES_LEQ_100, Some(25));

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

Creating a Primes<0> is a compile fail in const contexts and a panic otherwise.

Other functionality

Use is_prime to test whether a given number is prime

const CHECK: bool = is_prime(18_446_744_073_709_551_557);
assert!(CHECK);

or are_prime to compute the prime status of the N first integers,

const N: usize = 10;
const PRIME_STATUS: [bool; N] = are_prime();
//                        0      1      2     3     4      5     6      7     8      9
assert_eq!(PRIME_STATUS, [false, false, true, true, false, true, false, true, false, false]);

or are_prime_below to compute the prime status of the N largest integers below a given value,

const N: usize = 70711;
const BIG_PRIME_STATUS: [bool; N] = are_prime_below(5_000_000_031);
//                                     5_000_000_028  5_000_000_029  5_000_000_030
assert_eq!(BIG_PRIME_STATUS[N - 3..], [false,         true,          false]);

and more!

License

Licensed under either of

• Apache License, Version 2.0 LICENSE-APACHE
• MIT license LICENSE-MIT

at your option.

Contribution

Contributions are welcome!

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.