# Class: Prime

Inherits:
Object
• Object
show all
Extended by:
Enumerable, Forwardable
Includes:
Enumerable
Defined in:
lib/prime.rb

## Overview

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`Prime`.new is obsolete.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#prime? .

## Class Method Summary collapse

• Returns the default instance of Prime.

• :nodoc:.

## Instance Method Summary collapse

• Iterates the given block over all prime numbers.

• constructor

obsolete.

• Re-composes a prime factorization and returns the product.

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

• Returns the factorization of `value`.

## Constructor Details

### #initialize ⇒ Prime

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

 ``` 96 97 98 99 100``` ```# 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'lib/prime.rb', line 96 def initialize @generator = EratosthenesGenerator.new extend OldCompatibility warn "Prime::new is obsolete.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```

## Class Method Details

### .instance ⇒ Object

Returns the default instance of Prime.

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

:nodoc:

 ``` 108 109 110``` ```# File 'lib/prime.rb', line 108 def method_added(method) # :nodoc: (class<< self;self;end).def_delegator :instance, method end```

## Instance Method Details

### #each(ubound = nil, generator = EratosthenesGenerator.new, &block) ⇒ Object

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`.

 ``` 147 148 149 150``` ```# 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) ⇒ Object

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
``````
 ``` 182 183 184 185 186``` ```# 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) ⇒ Boolean

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

## Parameters

`value`

an arbitrary integer to be checked.

`generator`

optional. A pseudo-prime generator.

Returns:

• (Boolean)
 ``` 159 160 161 162 163 164 165 166 167``` ```# 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) ⇒ Object

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]]
``````

Raises:

• (ZeroDivisionError)
 ``` 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236``` ```# 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```