PRIME(S) \(\rightarrow\) EMIRP(S)Number Theory Level 3
An 'emirp' (prime spelled backward) is a prime whose digits when reversed, yields another prime. For example, 31 is an emirp of 13 and vice-versa. The definition of an emirp does not include palindromic primes such as 101 as they yield the same number when their digits are reversed.
Consider the unordered pair \((p_1 , p_2)\) where \(p_1\) and \(p_2\) are primes which are emirps to each other. How many such unordered pairs of emirps exist which are less than 1000?