Lab Four Solution | Python Fiddle

# isPalindrome: string -> bool
# return True if and only if the input string is a palindrome
def isPalindrome(s):
   index1 = 0
   index2 = len(s) - 1

while index1 < index2:
      if s[index1] != s[index2]:
         return False

index1 += 1
      index2 -= 1

return True

# noneDivisible: int, [int] -> bool
# return True if and only if the first input is not divisible by any number in the second input
def noneDivisible(n, nums):
   for x in nums:
      if n % x == 0:
         return False

return True

# primesBelow: int -> [int]
# return a list of primes less than the input integer
# note, there are many ways to make this function run MUCH faster, but 
# we don't yet care about efficiency in this class (just getting a working program)
def primesBelow(cap):
   if cap <= 2:
      return []
    
    primesSoFar = [2]

for num in xrange(3, cap, 2): # check only odd numbers
      if noneDivisible(num, primesSoFar):
         primesSoFar.append(num)

return primesSoFar

# palindomePrimesBelow: int -> [int]
# return a list of primes below the given input integer which are also palindromes
def palindromePrimesBelow(cap):
   return [x for x in primesBelow(cap) if isPalindrome(str(x))]

if __name__ == "__main__":
   from unittest import test

test(True, isPalindrome('abba'))
   test(True, isPalindrome('aba'))
   test(True, isPalindrome('abananaba'))
   test(False, isPalindrome('abxyba'))
   test(False, isPalindrome('xabbay'))

test(True, noneDivisible(9, [2,4,6,8]))
   test(False, noneDivisible(90, [2,5,9,11]))
   test(True, noneDivisible(13, [2,3,5,7,11]))

test([2], primesBelow(3))
   test([2,3,5,7], primesBelow(8))
   test([2,3,5], primesBelow(7))
   test([2,3,5,7,11,13,17,19], primesBelow(20))

test([2,3,5,7], palindromePrimesBelow(10))
   test([2,3,5,7], palindromePrimesBelow(11))
   test([2,3,5,7,11], palindromePrimesBelow(100))
   test([2,3,5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919,929,10301], palindromePrimesBelow(10302))

print "My tests pass!"

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