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, and currently supports Rust versions 1.67.1 or newer, though enabling feature flags may increase this.

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.count_primes_leq(100);
assert_eq!(PRIMES_LEQ_100, Some(25));

// Prime factorization:
assert_eq!(CACHE.prime_factorization(3072).collect(), &[(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.count_primes_leq(1000).is_none());

Want only the numbers? Use the primes function, or convert the cache into an array:

use const_primes::{primes, Primes};

const CACHE: Primes<10> = Primes::new();

const PRIMES_ARRAY1: [u32; 10] = primes();
const PRIMES_ARRAY2: [i32; 10] = PRIMES.into_array();

assert_eq!(PRIMES_ARRAY1, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]);
assert_eq!(PRIMES_ARRAY1, PRIMES_ARRAY2);

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);

The crate also provides prime generation and sieving functions that can be used to work with ranges that don't start at zero, e.g. primes_geq and sieve_lt. These functions can use large sieves to compute large primes, but don't need to return the entire sieve, just the requested numbers. They are most conveniently used through the macros primes_segment! and sieve_segment! that automatically compute the size of the sieve that's needed for a certain computation.

Compute 3 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]));

Find the next or previous prime numbers with next_prime and previous_prime if they exist and can be represented in a u64:

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!

std: implements the Error trait from the standard library for the error types.

serde: derives the Serialize and Deserialize traits from serde for the Primes struct, as well as a few others.

const_assert: promotes panics that involve only const generics into compile errors. Increases the MSRV of the crate to 1.79.0.

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

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.