const-primes 0.9.7

Work with prime numbers in const contexts. Prime generation, primality testing, prime counting, and more.
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# const-primes


[![Crates.io Version](https://img.shields.io/crates/v/const_primes?logo=rust)](https://crates.io/crates/const-primes)
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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](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Segmented_sieve)
and can be used as a cache of prime numbers for related computations:

```rust
// 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.prime_pi(1000).is_none());
```

## Example: primality checking


Use `is_prime` to test whether a given number is prime:

```rust
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 3 primes greater than or equal to 5000000031:

```rust
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`:

```rust
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`](https://crates.io/crates/serde)
for the `Primes` struct, as well as a few others.
Uses the [`serde_arrays`](https://crates.io/crates/serde_arrays)
crate to do this, and that crate uses the standard library.

`zerocopy`: derives the `IntoBytes` trait from [`zerocopy`](https://crates.io/crates/zerocopy)
for the `Primes` struct.

`rkyv`: derives the `Serialize`, `Deserialize`, and `Archive` traits from
[`rkyv`](https://crates.io/crates/rkyv) for the `Primes` struct.

`fast_test`: speeds up primality testing significantly by using the
[`machine-prime`](https://crates.io/crates/machine-prime) crate.

<br>

### License


<sup>
Licensed under either of <a href="LICENSE-APACHE">Apache License, Version
2.0</a> or <a href="LICENSE-MIT">MIT license</a> at your option.
</sup>

<br>

<sub>
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.
</sub>