class 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Prime.new is obsolete.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 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? .

Public Class Methods

instance() click to toggle source

Returns the default instance of Prime.

# File lib/prime.rb, line 106
def instance; @the_instance end

new() click to toggle source

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

# 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  warn "Prime::new is obsolete.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

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 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.

# 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) 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/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 lib/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 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]]

# File lib/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