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Class: Prime

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

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? .

Constant Summary

Class Method Summary

Instance Method Summary

Class Method Details

.method_added(method)

This method is for internal use only.
[ GitHub ] 

  


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



def method_added(method) # :nodoc:
  (class<< self;self;end).def_delegator :instance, method
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.




  



  [ GitHub ]


  

  


# File 'lib/prime.rb', line 212



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


  








  

    #include?(obj)  ⇒ Boolean 
  



  

    

Returns true if obj is an ::Integer and is prime.  Also returns true if obj is a Module that is an ancestor of Prime. Otherwise returns false.


  





  


  [ GitHub ]


  

  


# File 'lib/prime.rb', line 220



def include?(obj)
  case obj
  when Integer
    prime?(obj)
  when Module
    Module.instance_method(:include?).bind(Prime).call(obj)
  else
    false
  end
end


  








  

    #int_from_prime_division(pd)  
  



  

    

Re-composes a prime factorization and returns the product.



For the decomposition:



[[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.



Parameters


pd



Array of pairs of integers. Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).





Example



Prime.int_from_prime_division([[3, 2], [5, 1]])  #=> 45
3**2 * 5                                         #=> 45


  



  [ GitHub ]


  

  


# File 'lib/prime.rb', line 268



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. Integer#prime? is much more performant.



Parameters


value



an arbitrary integer to be checked.


generator



optional. A pseudo-prime generator.




  





  
Raises:


    
  
  • 
    (ArgumentError)
  
    • 





  [ GitHub ]


  

  


# File 'lib/prime.rb', line 238



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)  
  



  

    

Returns the factorization of value.



For an arbitrary integer:



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



prime_division returns an array of pairs of integers:



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



Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).



Parameters


value



An arbitrary integer.


generator



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





Exceptions


ZeroDivisionError



when value is zero.





Example



Prime.prime_division(45)  #=> [[3, 2], [5, 1]]
3**2 * 5                  #=> 45


  





  
Raises:


    
  
  • 
    (ZeroDivisionError)
  
    • 





  [ GitHub ]


  

  


# File 'lib/prime.rb', line 303



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