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This got around 11000 points using a limit of 13.5 million, in roughly 2 seconds

Basically my strategy is to create a lookup list out made of bools, where at the end of each cycle in my main loop, the next true value with a higher index than the current indexed value is guaranteed to be prime.

The first thing i do when I evaluate a new prime, is to eliminate its multiples from the rest of the list.

After that I get the reverse of my current prime value and perform:

• 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)