The set of all prime numbers.

## Example

Prime.each(100) do |prime| p prime #=> 2, 3, 5, 7, 11, ...., 97 end

Prime is Enumerable:

Prime.first 5 # => [2, 3, 5, 7, 11]

## Retrieving the instance

For convenience, each instance method of `Prime`.instance can be accessed as a class
method of `Prime`.

e.g.

Prime.instance.prime?(2) #=> true Prime.prime?(2) #=> true

## Generators

A “generator” provides an implementation of enumerating pseudo-prime numbers and it remembers the position of enumeration and upper bound. Furthermore, it is an external iterator of prime enumeration which is compatible with an Enumerator.

`Prime::PseudoPrimeGenerator`
is the base class for generators. There are few implementations of
generator.

`Prime::EratosthenesGenerator`-
Uses eratosthenes’ sieve.

`Prime::TrialDivisionGenerator`-
Uses the trial division method.

`Prime::Generator23`-
Generates all positive integers which are not divisible by either 2 or 3. This sequence is very bad as a pseudo-prime sequence. But this is faster and uses much less memory than the other generators. So, it is suitable for factorizing an integer which is not large but has many prime factors. e.g. for Prime#prime? .

#### Cheking if a number is prime?

It’s a class for generating an enumerator for prime numbers and traversing over them.

It’s really slow and will be replaced in ruby 1.9 with a faster one.

Note: if you just want to test whether a number is prime or not, you can use this piece of code:

class Fixnum def prime? ('1' * self) !~ /^1?$|^(11+?)\1+$/ end end 10.prime?