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

Example: generate primes at compile time

Generate arrays of prime numbers at compile time with the function primes which uses a segmented sieve of Eratosthenes:

use const_primes::primes;

const PRIMES: [u32; 10] = primes();

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

Example: use a cache of generated primes for related computations

The struct Primes is a wrapper around an array of primes 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::<Vec<_>>(), &[(2, 10), (3, 1)]);

// 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());

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: sieving

Sieve a range of numbers for their prime status with sieve:

use const_primes::sieve;

const PRIME_STATUS: [bool; 10] = sieve();

//                        0      1      2     3     4      5     6      7     8      9
assert_eq!(PRIME_STATUS, [false, false, true, true, false, true, false, true, false, false]);

Example: generate the three primes after 5000000031

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]));

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!

Feature flags

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 only involve const generics into compile errors. Increases the MSRV of the crate to 1.79.0.

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
  Call primes_geq or primes_lt, and automatically compute the memory requirement of the sieve.
• sieve_segment
  Call sieve_geq or sieve_lt, and automatically compute the memory requirement of the sieve.

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

• count_primes
  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.
• 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.
• 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.