new_contents: #!/usr/bin/env python
  #-*-coding:utf-8-*-
  
  '''
  Euler's Totient function, φ(n) [sometimes called the phi function],
  is used to determine the number of positive numbers less than or
  equal to n which are relatively prime to n.
  For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and
  relatively prime to nine, φ(9)=6.
  The number 1 is considered to be relatively prime to every positive number,
  so φ(1)=1.
  
  Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
  
  Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and
  the ratio n/φ(n) produces a minimum.
  '''
  
  import math
  import timeit
  
  
  def is_prime(n):
      for i in range(2, int(math.sqrt(n))+1):
          if n % i == 0:
              return False
      return True
  
  
  def next_prime(n):
      while True:
          n += 1
          if is_prime(n):
              return n
  
  
  def calc(n):
      prime = 1
      phi = 1
      while phi*prime <= n:
          phi *= prime
          prime = next_prime(prime)
      return phi
  
  
  if __name__ == '__main__':
      print calc(1000000)
      print timeit.Timer('problem_069.calc(1000000)', 'import problem_069').timeit(1)
  
subject: add problem 069