IsPrime

import time

def IsPrime(n):
  start = time.time()
  if n == 2:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return True
  if n == 3:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return True
  if n == 4:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return False
  if n == 5:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return True
  if n == 6:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return False
  if n > 6:
    bool = []
    for i in range(2, n//2+1):
      if n%i == 0:
        bool.append("True")
    if "True" in bool:
      end = time.time()
      print("The function took", str(end-start), "seconds.")
      return False
    else:
      end = time.time()
      print("The function took", str(end-start), "seconds.")
      return True
  else:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return False



def IsPrime_alternative(n):
  start = time.time()
  i=2
  if n<i:
    end = time.time()
    print("The function took", str(end-start), "seconds.")
    return False
  while i < n:
    if n%i==0:
      end = time.time()
      print("The function took", str(end-start), "seconds.")
      return False
    else:
      i+=1
  end = time.time()
  print("The function took", str(end-start), "seconds.")
  return True

difficult_to_divide_list = []
# check for a random number x if it is hard to divide (i.e. divisible only by numbers higher than 8). If yes, return True, else: return False
def check_boolean(x):
  bool = False # assume that it is not hard to divide

  while ~bool:

    if x%2 != 0:
      bool = True
    else:
      bool = False
      break
    if x%3 != 0:
      bool = True
    else:
      bool = False
      break
    if x%4 != 0:
      bool = True
    else:
      bool = False
      break
    if x%5 != 0:
      bool = True
    else:
      bool = False
      break
    if x%6 != 0:
      bool = True
    else:
      bool = False
      break
    if x%7 != 0:
      bool = True
    else:
      bool = False
      break
    if x%8 != 0:
      bool = True
    else:
      bool = False
      break
    break
  return bool


N = 1000

prime_list = []
for i in range(1,N):
  if IsPrime_alternative(i):
    prime_list.append(i)

def add_to_hard_divisors_list(N):
  for i in range(2,N):
    if check_boolean(i):
      difficult_to_divide_list.append(i)

add_to_hard_divisors_list(N)


def intersection(l1, l2):
  l3 = [value for value in l1 if value in l2]
  return l3
def overhang(l1, l2):
  l3 = [value for value in l1 if value not in intersection(l1,l2)]
  return l3

print("\n"+"This is the list of prime numbers: ")
print(prime_list)
print("\n"+"This is the list of difficult to divide numbers: ")
print(difficult_to_divide_list)
print("\n"+"This is the list of the junction: ")
print(intersection(difficult_to_divide_list, prime_list))
print("\n"+"This is the list of difficult to divide non-prime numbers: ")
print(overhang(difficult_to_divide_list, prime_list))