gistfile1.rb

require "set"

def eratosthenes n
  nums = [nil, nil, *2..n]
  (2..Math.sqrt(n)).each do |i|
    (i**2..n).step(i) { |m| nums[m] = nil } if nums[i]
  end

  nums.compact
end

def rotations number
  rotations = [number]

  digits = digits(number)
  (digits.size - 1).times do
    rotations << from_digits(digits.push(digits.shift))
  end

  rotations.uniq
end

def from_digits digits
  number = 0

  digits.reverse.each_with_index do |digit, power|
    number += digit * 10**power
  end

  number
end

def digits number
  digits = []

  while number > 0
    digits << number % 10
    number /= 10
  end

  digits.reverse
end

def solve n
  primes = eratosthenes(n).to_set
  primes.reject! { |prime| !rotations(prime).all? { |rotation| primes.include?(rotation) } }
  primes
end

puts solve(ARGV[0].to_i).size