Class: Prime

### Home Classes Methods

### In Files

- lib/backports/1.9.1/stdlib/prime.rb

### Parent

Object

### Namespace

- MODULE Prime::OldCompatibility
- CLASS Prime::EratosthenesGenerator
- CLASS Prime::EratosthenesSieve
- CLASS Prime::Generator23
- CLASS Prime::PseudoPrimeGenerator
- CLASS Prime::TrialDivision
- CLASS Prime::TrialDivisionGenerator

### Methods

- ::instance
- ::new
- #each
- #int_from_prime_division
- #prime?
- #prime_division

### Included Modules

- Enumerable

### Class/Module Index

Quicksearch

- Prime
- Prime::EratosthenesGenerator
- Prime::EratosthenesSieve
- Prime::Generator23
- Prime::OldCompatibility
- Prime::PseudoPrimeGenerator
- Prime::TrialDivision
- Prime::TrialDivisionGenerator
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- Backports::Random::Implementation
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# Prime

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`Prime`.new is obsolete.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? .

### Public Class Methods

instance() click to toggle source

Returns the default instance of Prime.

    # File lib/backports/1.9.1/stdlib/prime.rb, line 99
    def instance; @the_instance end

new() click to toggle source

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

    # File lib/backports/1.9.1/stdlib/prime.rb, line 89
    def initialize
      @generator = EratosthenesGenerator.new
      extend OldCompatibility
      warn "Prime::new is obsolete. use Prime::instance or class methods of Prime."
    end

### Public Instance Methods

each(ubound = nil, generator = EratosthenesGenerator.new, &block) click to toggle source

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`.

    # File lib/backports/1.9.1/stdlib/prime.rb, line 136
    def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
      generator.upper_bound = ubound
      generator.each(&block)
    end

int_from_prime_division(pd) click to toggle source

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

    # File lib/backports/1.9.1/stdlib/prime.rb, line 169
    def int_from_prime_division(pd)
      pd.inject(1){|value, (prime, index)|
        value *= prime**index
      }
    end

prime?(value, generator = Prime::Generator23.new) click to toggle source

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

## Parameters

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

    # File lib/backports/1.9.1/stdlib/prime.rb, line 147
    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
        return true if q < num
        return false if r == 0
      end
    end

prime_division(value, generator= Prime::Generator23.new) click to toggle source

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]]

    # File lib/backports/1.9.1/stdlib/prime.rb, line 196
    def prime_division(value, generator= Prime::Generator23.new)
      raise ZeroDivisionError if value == 0
      if value < 0
        value = -value
        pv = [[-1, 1]]
      else
        pv = []
      end
      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

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