# Class: Prime

Inherits:
Object
show all
Extended by:
Enumerable, Forwardable
Includes:
Enumerable
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``````

## Retrieving the instance

Prime.new is obsolete. Now Prime has the default instance and you can access it as Prime.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. Futhermore, it is a external iterator of prime enumeration which is compatible to an Enumerator.

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

Prime::EratosthenesGenerator

Uses eratosthenes's sieve.

Prime::TrialDivisionGenerator

Uses the trial division method.

Prime::Generator23

Generates all positive integers which is not divided by 2 nor 3. This sequence is very bad as a pseudo-prime sequence. But this is faster and uses much less memory than other generators. So, it is suitable for factorizing an integer which is not large but has many prime factors. e.g. for Prime#prime? .

## Constant Summary

### Constants included from Forwardable

Forwardable::FORWARDABLE_VERSION

## Class Method Summary (collapse)

• Returns the default instance of Prime.

• :nodoc:.

## Instance Method Summary (collapse)

• Iterates the given block over all prime numbers.

• constructor

obsolete.

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

• Returns true if value is prime, false for a composite.

• Returns the factorization of value.

to_set

## Constructor Details

### - (Prime) initialize

obsolete. Use Prime::instance or class methods of Prime.

 ``` 88 89 90 91 92``` ```# File 'lib/prime.rb', line 88 def initialize @generator = EratosthenesGenerator.new extend OldCompatibility warn "Prime::new is obsolete. use Prime::instance or class methods of Prime." end```

## Class Method Details

### + (Object) instance

Returns the default instance of Prime.

 ``` 98``` ```# File 'lib/prime.rb', line 98 def instance; @the_instance end```

### + (Object) method_added(method)

:nodoc:

 ``` 100 101 102``` ```# File 'lib/prime.rb', line 100 def method_added(method) # :nodoc: (class<

## Instance Method Details

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

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 yields all prime numbers p <= ubound.

## Note

Prime.new returns a object extended by Prime::OldCompatibility in order to compatibility to Ruby 1.8, and Prime#each is overwritten by Prime::OldCompatibility#each.

Prime.new is now obsolete. Use Prime.instance.each or simply Prime.each.

 ``` 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```

### - (Object) int_from_prime_division(pd)

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``
 ``` 169 170 171 172 173``` ```# File 'lib/prime.rb', line 169 def int_from_prime_division(pd) pd.inject(1){|value, (prime, index)| value *= prime**index } end```

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

Returns true if value is prime, false for a composite.

## Parameters

 value an arbitrary integer to be checked. generator optional. A pseudo-prime generator.

Returns:

• (Boolean)
 ``` 146 147 148 149 150 151 152 153 154 155``` ```# File 'lib/prime.rb', line 146 def prime?(value, generator = Prime::Generator23.new) value = -value if value < 0 return false if value < 2 for num in generator #q,r = value.divmod num q = value / num; r = value % num return true if q < num return false if r == 0 end end```

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

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 ascendent order. It must generate all prime numbers, but may generate non prime numbers.

### 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)
 ``` 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215``` ```# File 'lib/prime.rb', line 196 def prime_division(value, generator= Prime::Generator23.new) raise ZeroDivisionError if value == 0 pv = [] for prime in generator 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 return pv end```