Case1 If the reversed value is lower than the non reversed, I check to see if it is also a prime using my lookup list. If its also a prime value I only add the original value.

Case2 if reversed value is higher than my overall limit I perform a simple check on it using a common prime evaluating function. If it is prime I add the non reversed prime

Case3 If the reversed value higher than the non reversed prime and lower than the limit I will ignore it seeing as it will be found again under Case1

 from time import time
 def is_prime(n):
     for i in xrange(2, int(math.sqrt(n)) + 1):
         if n % i == 0:
             return False
     return True
 def DoMath(limit):
     start = time()
     lkup = [True,True,True] +[ bool(ii%2) for ii in xrange(3,limit)]
     with open("text.txt", 'w') as file:
         index = 3
         r_index = 0
         str_index = ''
         while index <  limit:
             for ii in xrange(index*2, limit, index):
                 lkup[ii] = False
             str_index = str(index)
             r_index = int(str_index[::-1])
             if r_index >= limit and is_prime(r_index):
                 file.write(str_index+'\n')
             elif r_index < index and lkup[r_index]:
                 file.write(str_index+'\n')
             index += 1
             try:
                 while not lkup[index]:
                     index += 1
             except IndexError:
                 break
     end=time()
     print("Time Taken : ",end-start)

Case1 If the reversed value is lower than the non reversed, I check to see if it is also a prime using my lookup list. If its also a prime value I only add the original value.

Case2 if reversed value is higher than my overall limit I perform a simple check on it using a common prime evaluating function. If it is prime I add the non reversed prime

Case3 If the reversed value higher than the non reversed prime and lower than the limit I will ignore it seeing as it will be found again under Case1

 from time import time
 def is_prime(n):
     for i in xrange(2, int(math.sqrt(n)) + 1):
         if n % i == 0:
             return False
     return True
 def DoMath(limit):
     start = time()
     lkup = [True,True,True] +[ bool(ii%2) for ii in xrange(3,limit)]
     with open("text.txt", 'w') as file:
         index = 3
         r_index = 0
         str_index = ''
         while index <  limit:
             if lkup[index]:
                 for ii in xrange(index*2, limit, index):
                     lkup[ii] = False
                 str_index = str(index)
                 r_index = int(str_index[::-1])
                 if r_index >= limit and is_prime(r_index):
                     file.write(str_index+'\n')
                 elif r_index < index and lkup[r_index]:
                     file.write(str_index+'\n')
             index += 1
     end=time()
     print("Time Taken : ",end-start)

Case1 If the reversed value is lower than the non reversed, I check to see if it is also a prime using my lookup list. If its also a prime value I only add the original value.

Case2 if reversed value is higher than my overall limit I perform a simple check on it using a common prime evaluating function. If it is prime I add the non reversed prime

Case3 If the reversed value higher than the non reversed prime and lower than the limit I will ignore it seeing as it will be found again under Case1

 from time import time
 def is_prime(n):
     for i in xrange(2, int(math.sqrt(n)) + 1):
         if n % i == 0:
             return False
     return True
 def DoMath(limit):
     start = time()
     lkup = [True,True,True] +[ bool(ii%2) for ii in xrange(3,limit)]
     with open("text.txt", 'w') as file:
         index = 3
         r_index = 0
         str_index = ''
         while index <  limit:
             for ii in xrange(index*2, limit, index):
                 lkup[ii] = False
             str_index = str(index)
             r_index = int(str_index[::-1])
             if r_index > index and r_index >= limit and is_prime(r_index):
                 file.write(str_index+'\n')
             elif r_index < index and lkup[r_index]:
                 file.write(str_index+'\n')
             index += 1
             try:
                 while not lkup[index]:
                     index += 1
             except IndexError:
                 break
     end=time()
     print("Time Taken : ",end-start)

Case1 If the reversed value is lower than the non reversed, I check to see if it is also a prime using my lookup list. If its also a prime value I only add the original value.

Case2 if reversed value is higher than my overall limit I perform a simple check on it using a common prime evaluating function. If it is prime I add the non reversed prime

Case3 If the reversed value higher than the non reversed prime and lower than the limit I will ignore it seeing as it will be found again under Case1

 from time import time
 def is_prime(n):
     for i in xrange(2, int(math.sqrt(n)) + 1):
         if n % i == 0:
             return False
     return True
 def DoMath(limit):
     start = time()
     lkup = [True,True,True] +[ bool(ii%2) for ii in xrange(3,limit)]
     with open("text.txt", 'w') as file:
         index = 3
         r_index = 0
         str_index = ''
         while index <  limit:
             for ii in xrange(index*2, limit, index):
                 lkup[ii] = False
             str_index = str(index)
             r_index = int(str_index[::-1])
             if r_index >= limit and is_prime(r_index):
                 file.write(str_index+'\n')
             elif r_index < index and lkup[r_index]:
                 file.write(str_index+'\n')
             index += 1
             try:
                 while not lkup[index]:
                     index += 1
             except IndexError:
                 break
     end=time()
     print("Time Taken : ",end-start)