#!/usr/bin/ruby require 'prime' # https://github.com/ChapterHouse/prime_miller_rabin # Copyright (c) 2013 Frank Hall # MIT License class Prime::MillerRabin < Prime::PseudoPrimeGenerator def succ() self.last_prime = next_prime(last_prime || 1) end def rewind() self.last_prime = nil end def prime?(x) miller_rabin(x) end private attr_accessor :last_prime def likely_prime?(a, n) d = n - 1 s = 0 while d % 2 == 0 do d >>= 1 s += 1 end b = 1 while d > 0 u = d % 2 t = d / 2 b = (b * a) % n if u == 1 a = a**2 % n d = t end if b == 1 true else s.times do |i| return true if b == n - 1 b = (b * b) % n end (b == n - 1) end end def miller_rabin(n) if n.abs < 2 false else likely_prime = true # 26 Yields a probability of prime at 99.99999999999998% so lets kick it up a notch. 27.times do |i| begin a = rand(n) end while a == 0 likely_prime = likely_prime?(a, n) break unless likely_prime end likely_prime end end def next_prime(x) if x < 2 2 elsif x < 3 3 elsif x < 5 5 else x += (x.even? ? 1 : (x % 10 == 3 ? 4 : 2 )) x += (x % 10 == 3 ? 4 : 2 ) until x.prime? x end end end N=gets.to_i if N>25 p N%8==1&&Prime::MillerRabin.new.prime?(N-8) ? 14 : 8 else h={4=>3,6=>5,12=>11,14=>13,18=>8,20=>19,21=>19,24=>23,25=>23};h.default=7 p h[N] end