text: """
  The prime HP reached starting from a number , concatenating its prime factors, and repeating until a prime is reached.
  If you have doubts, refer the article here [http://mathworld.wolfram.com/HomePrime.html]
  
  write a function to calculate the HP of a given number.
  
  Also write a function to compute the Euclid-Mullin sequence [http://mathworld.wolfram.com/Euclid-MullinSequence.html].
  """
  
  import numpy as np
  
  
  def is_prime(n):
      """https://stackoverflow.com/questions/15285534/isprime-function-for-python-language"""
      if n == 2 or n == 3: return True
      if n < 2 or n%2 == 0: return False
      if n < 9: return True
      if n%3 == 0: return False
      r = int(n**0.5)
      f = 5
      while f <= r:
          if n%f == 0: return False
          if n%(f+2) == 0: return False
          f +=6
      return True
  
  
  def factorize(n):
      active_num = n
  
      factors = []
      n = 2
      while active_num != 1:
          if active_num % n == 0:
              active_num /= n
              factors.append(str(n))
          else:
              n += 1
      return factors
  
  
  def home_prime(n):
      while not is_prime(n):
          n = int(''.join(factorize(n)))
      return n
  
  
  def euclid_mullin(n):
      e_m = []
      for i in range(n):
          e_m.append(int(factorize(np.prod(e_m)+1)[0]))
          print(e_m)
      return e_m
  
  if __name__ == '__main__':
      print(home_prime(5))
      euclid_mullin(9)