“primes-utils” is a Rubygem which provides a suite of extremely fast

(relative to Ruby’s standard library) utility methods for testing and

generating primes.

Install it the usual way:

```
$ gem install primes-utils
```

Then require inside ruby as:

```
> require 'primes/utils'
```

The suite consists of the following methods:

1)prime?

Determine if the absolute value of an integer is prime. Return ‘true’

or ‘false’.

This replaces the `prime?`

method in the `prime.rb`

standard library.

2)primemr?(k=20)

Determine if the absolute value of an integer is prime using

Miller-Rabin test. Return ‘true’ or ‘false’.

Miller-Rabin here is super fast, but probabilistic (not deterministic),

primality test.

https://en.wikipedia.org/wiki/Miller-Rabin_primality_test

The method’s reliability can be increased by increasing the default

input parameter of k=20.

3)factors(p=13) or prime_division(p=13)

Determine the prime factorization of the absolute value of an integer.

This replaces the `prime division`

method in the `prime.rb`

standard

library.

Returns an array of arrays of factors and exponents: [[2,4],[3,2],[5,1]]

=> (2^4)(3^2)(5^1) = (16)(9)(5) = 720

Default Strictly Prime (SP) Prime Generator (PG) used here is P13.

Can change SP PG used on input. Acceptable primes range (3 - 19).

4)primes(start_num=0)

Create an array of primes from the absolute value range (|start_num| -

|end_num|).

The order of the range doesn’t matter if both given: start.primes end

<=> end.prime start

If only one parameter used, then all the primes upto that number will be

returned.

5)primenth(p=11) or nthprime(p=11)

Return the value of the nth (absolute value) prime.

Default Strictly Prime (SP) Prime Generator (PG) used here is P11.

Can change SP PG used on input. Acceptable primes range (3 - 19).

Coding Implementations

The methods `primemr`

, `nthprime/primenth`

, and `primes`

are coded in

pure ruby. The methods `prime?`

and `prime_division/factors`

have two

implementations. Each has a pure ruby implementation, and also a hybrid

implementation which uses the Unix cli command `factor`

if its available

on the host OS. `factor`

[5] is an extremely fast C coded factoring

algorithm, part of the GNU Core Utilities package [4].

Upon loading, the gem tests if the desired `factor`

command exists on

the host OS. If so, it wraps a system call to it and uses it for

`prime?`

and `prime_division/factors`

. If not, it uses a fast pure ruby

implementation for each method based on the Sieve of Zakiya

(SoZ)[1][2][3].

References

[1]https://www.scribd.com/doc/150217723/Improved-Primality-Testing-and-Factorization-in-Ruby-revised

[2]https://www.scribd.com/doc/228155369/The-Segmented-Sieve-of-Zakiya-SSoZ

[3]https://www.scribd.com/doc/73385696/The-Sieve-of-Zakiya

[4]https://en.wikipedia.org/wiki/GNU_Core_Utilities

[5]https://en.wikipedia.org/wiki/Factor_(Unix)

Author

Jabari Zakiya