prime?

prime.rb

require 'prime'
require 'benchmark'

def isqrt(n)
  n = n.to_i
  x = n
  y = (x + 1) / 2
  while y < x
    x = y
    y = (x + n / x) / 2
  end
  x
end

def prime? (n)
  return false if n<1
  return true if [2,3].include?(n)
  return false if n % 2 == 0 || n % 3 == 0
  i = 1
  x = 6
  n_2 = isqrt(n)
  while (x <= n_2)
    return false if n % (x-1) == 0 || n % (x+1) == 0
    i += 1
    x = 6*i
  end
  true
end

n = 1090109110921093
Benchmark.bm do |r|
  10.times do
    r.report {puts n.prime?}
    r.report {puts prime?(n)}
  end
end

This is the version of prime? in prime.rb used in 2.3.0.

class Integer
      def prime?
        return self >= 2 if self <= 3
        return false if self % 2 == 0 or self % 3 == 0
        (5..(self**0.5).floor).step(6).each do |i|
          if self % i == 0 || self % (i + 2) == 0
            return false
          end
        end
        true
      end
end

For the math behind this see the primes-utils rubygem, and its PRIMES-UTILS HANDBOOK.

https://www.scribd.com/doc/266461408/Primes-Utils-Handbook