`123456789_123456789_123456789_123456789_123456789_`

# Class: Prime

 Relationships & Source Files Namespace Children Classes: Super Chains via Extension / Inclusion / Inheritance Class Chain: self, Enumerable, Forwardable Instance Chain: self, Singleton, Enumerable Inherits: Object 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? .

## Class Method Summary

• Internal use only

## Instance Method Summary

• 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

This method is for internal use only.
[ GitHub ]

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

## Instance Method Details

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

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`.

[ GitHub ]

`# File 'lib/prime.rb', line 139`
```
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.

[ GitHub ]

`# File 'lib/prime.rb', line 147`
```
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)

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``````
[ GitHub ]

`# File 'lib/prime.rb', line 194`
```
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.

#### Parameters

`value`

an arbitrary integer to be checked.

`generator`

optional. A pseudo-prime generator.

Raises:

• (`ArgumentError`)
[ GitHub ]

`# File 'lib/prime.rb', line 164`
```
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)

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`)
[ GitHub ]

`# File 'lib/prime.rb', line 229`
```
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
```