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¶ ↑

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? .

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.

# File lib/prime.rb, line 135
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 171
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 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 147
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) 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 201
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