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)