In Files

  • prime.rb

Prime

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Prime.new is obsolete.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 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? .

Public Class Methods

new() click to toggle source

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

 
               # File 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  warn "Prime::new is obsolete.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
            

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 prime.rb, line 147
def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
  generator.upper_bound = ubound
  generator.each(&block)
end
            
instance() click to toggle source

Returns the default instance of Prime.

 
               # File prime.rb, line 106
def instance; @the_instance 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 prime.rb, line 182
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 prime.rb, line 159
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 prime.rb, line 212
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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