Determine all prime, palindrome string integers within a range
One suggestion: That sqrt is expensive, and you can eliminate it in a lot of common cases. For example: if any number except 2 is even, then it's not prime. Every second time you call check_prime, you're passing an even number. 

So you can check n%2 before the loop, and eliminate that sqrt on half of your calls. You can extend this to check the first few primes explicitly, before starting your loop:

def check_prime(n):
    if n&lt;2:
        return False
    if n%2==0:
        return n==2
    if n%3==0:
        return n==3
    if n%5==0:
        return n==5
    for i in range(7, int(sqrt(n))+1, 2):
        if n%i == 0:
            return False
    return True


You get diminishing returns by adding more checks. I benchmarked the above at about 2x as fast as your original code.