# Class: Prime

Inherits:
Object
• Object
show all
Extended by:
Enumerable, Forwardable
Includes:
Enumerable, Singleton
Defined in:
lib/prime.rb

## Overview

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? .

• :nodoc:.

## Instance Method Summary collapse

• Iterates the given block over all prime numbers.

• Re-composes a prime factorization and returns the product.

• Returns true if `value` is a prime number, else returns false.

• Returns the factorization of `value`.

## Class Method Details

### .method_added(method) ⇒ Object

:nodoc:

 ``` 104 105 106``` ```# File 'lib/prime.rb', line 104 def method_added(method) # :nodoc: (class<< self;self;end).def_delegator :instance, method end```

## Instance Method Details

### #each(ubound = nil, generator = EratosthenesGenerator.new, &block) ⇒ Object

Iterates the given block over all prime numbers.

## Parameters

`ubound`

Optional. An arbitrary positive number. The upper bound of enumeration. The method enumerates prime numbers infinitely if `ubound` is nil.

`generator`

Optional. An implementation of pseudo-prime generator.

## Return value

An evaluated value of the given block at the last time. Or an enumerator which is compatible to an `Enumerator` if no block given.

## Description

Calls `block` once for each prime number, passing the prime as a parameter.

`ubound`

Upper bound of prime numbers. The iterator stops after it yields all prime numbers p <= `ubound`.

 ``` 135 136 137 138``` ```# File 'lib/prime.rb', line 135 def each(ubound = nil, generator = EratosthenesGenerator.new, &block) generator.upper_bound = ubound generator.each(&block) end```

### #int_from_prime_division(pd) ⇒ Object

Re-composes a prime factorization and returns the product.

## Parameters

`pd`

Array of pairs of integers. The each internal pair consists of a prime number – a prime factor – and a natural number – an exponent.

## Example

For `[[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]]`, it returns:

``````p_1**e_1 * p_2**e_2 * .... * p_n**e_n.

Prime.int_from_prime_division([[2,2], [3,1]])  #=> 12
``````
 ``` 171 172 173 174 175``` ```# File 'lib/prime.rb', line 171 def int_from_prime_division(pd) pd.inject(1){|value, (prime, index)| value * prime**index } end```

### #prime?(value, generator = Prime::Generator23.new) ⇒ Boolean

Returns true if `value` is a prime number, else returns false.

## Parameters

`value`

an arbitrary integer to be checked.

`generator`

optional. A pseudo-prime generator.

Returns:

• (Boolean)

Raises:

• (ArgumentError)
 ``` 147 148 149 150 151 152 153 154 155 156``` ```# File 'lib/prime.rb', line 147 def prime?(value, generator = Prime::Generator23.new) raise ArgumentError, "Expected a prime generator, got #{generator}" unless generator.respond_to? :each raise ArgumentError, "Expected an integer, got #{value}" unless value.respond_to?(:integer?) && value.integer? return false if value < 2 generator.each do |num| q,r = value.divmod num return true if q < num return false if r == 0 end end```

### #prime_division(value, generator = Prime::Generator23.new) ⇒ Object

Returns the factorization of `value`.

## Parameters

`value`

An arbitrary integer.

`generator`

Optional. A pseudo-prime generator. `generator`.succ must return the next pseudo-prime number in the ascending order. It must generate all prime numbers, but may also generate non prime numbers too.

### Exceptions

`ZeroDivisionError`

when `value` is zero.

## Example

For an arbitrary integer:

``````n = p_1**e_1 * p_2**e_2 * .... * p_n**e_n,
``````

prime_division(n) returns:

``````[[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]].

Prime.prime_division(12) #=> [[2,2], [3,1]]
``````

Raises:

• (ZeroDivisionError)
 ``` 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225``` ```# File 'lib/prime.rb', line 201 def prime_division(value, generator = Prime::Generator23.new) raise ZeroDivisionError if value == 0 if value < 0 value = -value pv = [[-1, 1]] else pv = [] end generator.each do |prime| count = 0 while (value1, mod = value.divmod(prime) mod) == 0 value = value1 count += 1 end if count != 0 pv.push [prime, count] end break if value1 <= prime end if value > 1 pv.push [value, 1] end pv end```