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 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(), &[(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);

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 functions that can be used to work with ranges of large numbers 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]));

Example: find the next or previous prime numbers

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!

Features

serde: derives the Serialize and Deserialize traits from serde 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 zerocopy for the Primes struct.

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

License