# Crate slow_primes [−] [src]

Simplistic and relatively unoptimised handling of basic tasks around primes:

- checking for primality
- enumerating primes
- factorising numbers
- estimating upper and lower bounds for π(
*n*) (the number of primes below*n*) and*p*(the_{k}*k*th prime)

This uses a basic Sieve of Eratosthenes to enumerate the primes up to some fixed bound (in a relatively memory efficient manner), and then allows this cached information to be used for things like enumerating the primes, and factorisation via trial division.

(Despite the name, it can sieve the primes up to 10^{9} in
about 5 seconds.)

# Example

Let's find the 10001st prime. The basic idea is to enumerate the primes and then take the 10001st in that list.

Unfortunately, `Primes::sieve`

takes an upper bound, and it gives
us no information beyond this; so we really need some way to find
an upper bound to be guaranteed to include the 10001st prime. If
we had an a priori number we could just use that, but we don't
(for the purposes of this example, anyway). Hence, we can either
try filtering with exponentially larger upper bounds until we find
one that works (e.g. doubling each time), or just take a shortcut
and use deeper mathematics via
`estimate_nth_prime`

.

// find our upper bound let (_lo, hi) = slow_primes::estimate_nth_prime(10001); // find the primes up to this upper bound let sieve = slow_primes::Primes::sieve(hi as usize); // (.nth is zero indexed.) match sieve.primes().nth(10001 - 1) { Some(p) => println!("The 10001st prime is {}", p), // 104743 None => unreachable!(), }

# Using this library

Just add the following to your `Cargo.toml`

:

```
[dependencies.slow_primes]
git = "https://github.com/huonw/slow_primes"
```

## Structs

PrimeIterator |
Iterator over the primes stored in a sieve. |

Primes |
Stores information about primes up to some limit. |

StreamingSieve |
A segmented sieve that yields only a small run of primes at a time. |

## Functions

as_perfect_power |
Returns integers |

as_prime_power |
Return |

estimate_nth_prime |
Gives estimated bounds for `n` th prime number,
1-indexed (i.e. p = 2, _{1}p = 3)._{2} |

estimate_prime_pi |
Returns estimated bounds for π( |

is_prime_miller_rabin |
Test if |

## Type Definitions

Factors |
(prime, exponent) pairs storing the prime factorisation of a number. |