# Class: Prime

Inherits:
Object
• Object
show all
Extended by:
Enumerable, Forwardable
Includes:
Enumerable, Singleton
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

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? .

## Constant Summary collapse

VERSION =
`"0.1.2"`

• :nodoc:.

## Instance Method Summary collapse

• Iterates the given block over all prime numbers.

• Returns true if `obj` is an Integer and is prime.

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

• Returns true if `value` is a prime number, else returns false.

• Returns the factorization of `value`.

## Class Method Details

:nodoc:

 ``` 181 182 183``` ```# File 'lib/prime.rb', line 181 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`.

 ``` 212 213 214 215``` ```# File 'lib/prime.rb', line 212 def each(ubound = nil, generator = EratosthenesGenerator.new, &block) generator.upper_bound = ubound generator.each(&block) end```

### #include?(obj) ⇒ Boolean

Returns true if `obj` is an Integer and is prime. Also returns true if `obj` is a Module that is an ancestor of `Prime`. Otherwise returns false.

Returns:

• (Boolean)
 ``` 220 221 222 223 224 225 226 227 228 229``` ```# File 'lib/prime.rb', line 220 def include?(obj) case obj when Integer prime?(obj) when Module Module.instance_method(:include?).bind(Prime).call(obj) else false end end```

### #int_from_prime_division(pd) ⇒ Object

Re-composes a prime factorization and returns the product.

For the decomposition:

``````[[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.
``````

## Parameters

`pd`

Array of pairs of integers. Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).

## Example

``````Prime.int_from_prime_division([[3, 2], [5, 1]])  #=> 45
3**2 * 5                                         #=> 45
``````
 ``` 268 269 270 271 272``` ```# File 'lib/prime.rb', line 268 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 a prime number, else returns false. Integer#prime? is much more performant.

## Parameters

`value`

an arbitrary integer to be checked.

`generator`

optional. A pseudo-prime generator.

Returns:

• (Boolean)

Raises:

• (ArgumentError)
 ``` 238 239 240 241 242 243 244 245 246 247``` ```# File 'lib/prime.rb', line 238 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) ⇒ Object

Returns the factorization of `value`.

For an arbitrary integer:

``````p_1**e_1 * p_2**e_2 * ... * p_n**e_n,
``````

prime_division returns an array of pairs of integers:

``````[[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]].
``````

Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).

## Parameters

`value`

An arbitrary integer.

`generator`

Optional. A pseudo-prime generator. `generator`.succ must return the next pseudo-prime number in ascending order. It must generate all prime numbers, but may also generate non-prime numbers, too.

### Exceptions

`ZeroDivisionError`

when `value` is zero.

## Example

``````Prime.prime_division(45)  #=> [[3, 2], [5, 1]]
3**2 * 5                  #=> 45
``````

Raises:

• (ZeroDivisionError)
 ``` 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327``` ```# File 'lib/prime.rb', line 303 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```