class Prime

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

Returns the default instance 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  warn "Prime::new is obsolete.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

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

# File lib/prime.rb, line 147
def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
  generator.upper_bound = ubound
  generator.each(&block)
end

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 181
def int_from_prime_division(pd)
  pd.inject(1){|value, (prime, index)|
    value * prime**index
  }
end

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 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

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.

# 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

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]]