Class Prime
In: lib/backports/1.9.1/stdlib/prime.rb
Parent: Object

The set of all prime numbers.

Example

 Prime.each(100) do |prime|
   p prime  #=> 2, 3, 5, 7, 11, ...., 97
 end

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Prime.new is obsolete.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. 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.

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#prime? .

Methods

Included Modules

Enumerable Enumerable

Classes and Modules

Module Prime::OldCompatibility
Class Prime::EratosthenesGenerator
Class Prime::EratosthenesSieve
Class Prime::Generator23
Class Prime::PseudoPrimeGenerator
Class Prime::TrialDivision
Class Prime::TrialDivisionGenerator

Public Class methods

Returns the default instance of Prime.

[Source]

    # File lib/backports/1.9.1/stdlib/prime.rb, line 98
98:     def instance; @the_instance end

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

[Source]

    # File lib/backports/1.9.1/stdlib/prime.rb, line 88
88:   def initialize
89:     @generator = EratosthenesGenerator.new
90:     extend OldCompatibility
91:     warn "Prime::new is obsolete. use Prime::instance or class methods of Prime."
92:   end

Public Instance methods

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 Primeeach is overwritten by Prime::OldCompatibility#each.

Prime.new is now obsolete. Use Prime.instance.each or simply Prime.each.

[Source]

     # File lib/backports/1.9.1/stdlib/prime.rb, line 135
135:   def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
136:     generator.upper_bound = ubound
137:     generator.each(&block)
138:   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

[Source]

     # File lib/backports/1.9.1/stdlib/prime.rb, line 168
168:   def int_from_prime_division(pd)
169:     pd.inject(1){|value, (prime, index)|
170:       value *= prime**index
171:     }
172:   end

Returns true if value is prime, false for a composite.

Parameters

value:an arbitrary integer to be checked.
generator:optional. A pseudo-prime generator.

[Source]

     # File lib/backports/1.9.1/stdlib/prime.rb, line 146
146:   def prime?(value, generator = Prime::Generator23.new)
147:     value = -value if value < 0
148:     return false if value < 2
149:     for num in generator
150:       q,r = value.divmod num
151:       return true if q < num
152:       return false if r == 0
153:     end
154:   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 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]]

[Source]

     # File lib/backports/1.9.1/stdlib/prime.rb, line 195
195:   def prime_division(value, generator= Prime::Generator23.new)
196:     raise ZeroDivisionError if value == 0
197:     if value < 0
198:       value = -value
199:       pv = [[-1, 1]]
200:     else
201:       pv = []
202:     end
203:     for prime in generator
204:       count = 0
205:       while (value1, mod = value.divmod(prime)
206:              mod) == 0
207:         value = value1
208:         count += 1
209:       end
210:       if count != 0
211:         pv.push [prime, count]
212:       end
213:       break if value1 <= prime
214:     end
215:     if value > 1
216:       pv.push [value, 1]
217:     end
218:     return pv
219:   end

[Validate]