<|system|>
How many prime numbers between 30 and 65 have a prime remainder when divided by 10?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
If a prime number between 30 and 65 has a prime remainder when divided by 10, it must end in 3 or 7, since any number greater than 10 ending in 2 or 5 is composite.  Systemically checking all possibilities, we see that the only such primes are 37, 43, 47, and 53, which gives us a total of $4$ such numbers.