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Class: Prime

Relationships & Source Files
Namespace Children
Modules:
OldCompatibility
Classes:
EratosthenesGenerator, EratosthenesSieve, Generator23, PseudoPrimeGenerator, TrialDivision, TrialDivisionGenerator
Super Chains via Extension / Inclusion / Inheritance
Class Chain:
self, Enumerable, Forwardable
Instance Chain:
self, Enumerable
Inherits: Object
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

Prime.new is obsolete.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. 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? .

Class Method Summary

Instance Method Summary

Constructor Details

.new ⇒ Prime

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

[ GitHub ] 

  


# File 'lib/prime.rb', line 96



def initialize
  @generator = EratosthenesGenerator.new
  extend OldCompatibility
  warn "Prime::new is obsolete. use Prime::instance or class methods of Prime."
end


  







Class Method Details



  

    .instance  
  



  

    

Returns the default instance of Prime.


  



  [ GitHub ]


  

  


# File 'lib/prime.rb', line 106



def instance; @the_instance end


  







Instance Method Details



  

    #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 it yields all prime numbers p <= ubound.





Note



Prime.new returns an object extended by Prime::OldCompatibility in order to be compatible with 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.


  



  [ GitHub ]


  

  


# File 'lib/prime.rb', line 147



def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
  generator.upper_bound = ubound
  generator.each(&block)
end


  








  

    #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


  



  [ GitHub ]


  

  


# File 'lib/prime.rb', line 181



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.




  





  


  [ GitHub ]


  

  


# File 'lib/prime.rb', line 159



def prime?(value, generator = Prime::Generator23.new)
  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)  
  



  

    

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)
  
    • 





  [ GitHub ]


  

  


# File 'lib/prime.rb', line 211



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