The set of all prime numbers.
Prime.each(100) do |prime| p prime #=> 2, 3, 5, 7, 11, ...., 97 end
Prime.new is obsolete.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
A "generator" provides an implementation of enumerating pseudo-prime numbers and it remembers the position of enumeration and upper bound. Futhermore, 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.
Uses eratosthenes's sieve.
Uses the trial division method.
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#prime? .
Returns the default instance of Prime.
# File lib/backports/1.9.1/stdlib/prime.rb, line 99 def instance; @the_instance end
Iterates the given block over all prime numbers.
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. |
An evaluated value of the given block at the last time. Or an enumerator which is compatible to an Enumerator if no block given.
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. |
Prime.new returns a object extended by Prime::OldCompatibility in order to compatibility to Ruby 1.8, and Primeeach is overwritten by Prime::OldCompatibility#each.
Prime.new is now obsolete. Use Prime.instance.each or simply Prime.each.
# File lib/backports/1.9.1/stdlib/prime.rb, line 136 def each(ubound = nil, generator = EratosthenesGenerator.new, &block) generator.upper_bound = ubound generator.each(&block) end
Re-composes a prime factorization and returns the product.
pd |
Array of pairs of integers. The each internal pair consists of a prime number -- a prime factor -- and a natural number -- an exponent. |
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/backports/1.9.1/stdlib/prime.rb, line 169 def int_from_prime_division(pd) pd.inject(1){|value, (prime, index)| value *= prime**index } end
Returns true if value is prime, false for a composite.
value |
an arbitrary integer to be checked. |
generator |
optional. A pseudo-prime generator. |
# File lib/backports/1.9.1/stdlib/prime.rb, line 147 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
Returns the factorization of value.
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. |
ZeroDivisionError |
when value is zero. |
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/backports/1.9.1/stdlib/prime.rb, line 196 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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