class

Crypto::Prime

Inherits Enumerable / Reference / Object

The set of all prime numbers. Adapted from the Ruby implementation at https://github.com/ruby/prime.

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]

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 methods

coprime?(a, b)

Returns true if the integer a is coprime (relatively prime) to integer b.

Example

RSA::Math.coprime?(6, 35) # => true
RSA::Math.coprime?(6, 27) # => false
Source
each(ubound = nil, generator = EratosthenesGenerator.new, &block : Int::Signed -> )

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.

Source
factorize(value, generator = Generator23.new)

Returns the factorization of value.

For an arbitrary integer:

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

factorize 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
`DivisionByZeroError`: when `value` is zero.

## Example

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

Source
int_from_factorization(pd : Indexable(Indexable(Int)))

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_factorization([[3, 2], [5, 1]]) # => 45
3**2 * 5                                       # => 45
Source
prime?(n, k = 10)

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

== Parameters

value: an arbitrary integer to be checked.

Source
random(start, stop, count, generator = Generator23.new, random = Random::DEFAULT)

Return count random primes in the given range.

Source
random(bits, random = Random::DEFAULT)
Source

Instance methods

each(ubound = nil, generator = EratosthenesGenerator.new, &block : Int::Signed -> )

see .each

Source
factorize(value, generator = Generator23.new)

see .factorize

Source
int_from_factorization(pd : Indexable(Indexable(Int)))

see .int_from_factorization

Source
prime?(n, k = 10)

see .prime?

Source
random(start, stop, count, generator = Generator23.new, random = Random::DEFAULT)

see .random

Source
random(bits, random = Random::DEFAULT)
Source

Nested types