Primacy

Check for and generate prime numbers

Installation

If available in Hex, the package can be installed by adding primacy to your list of dependencies in mix.exs:

def deps do
  [
    {:primacy, "~> 0.2.0"}
  ]
end

Usage

iex> Primacy.is_prime?(123_456_794_333)
true

iex> Primacy.is_prime?(123_456_794_334)
false

iex> Primacy.primes_near(600, count: 10)
[571, 577, 587, 593, 599, 601, 607, 613, 617, 619]

iex> Primacy.primes_near(600, count: 5, dir: :below)
[571, 577, 587, 593, 599]

iex> Primacy.primes_near(3, count: 5, dir: :below)
[2, 3]

primes_near/2 options:

• count: how many primes to return (default: 1)
• dir: :below, :above, or :around (default: :around)

Scanning downward stops at 2, so fewer than count primes may be returned. A count of zero or less returns an empty list.

Performance

is_prime?/1 uses 6k ± 1 trial division below 4,000,000 and Miller-Rabin above that, with deterministic witnesses below 2^{64. A prime at or above 2}64 is confirmed by exhaustive trial division, which can take several seconds. primes_near/2 walks 6k ± 1 candidates instead of every integer.

Sample results on an Apple M5 from mix bench, comparing against the plain trial-division baseline (labeled old):

Development

• mix test runs the test suite
• mix test --include slow adds the check for a prime above 2^64 (about 35 s)
• mix bench runs the benchee benchmark suite

Documentation

Documentation can be generated with ExDoc and published on HexDocs. Once published, the docs can be found at https://hexdocs.pm/primacy.