PRIME(S) EMIRP(S)
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 where and are primes which are emirps to each other. How many such unordered pairs of emirps exist which are less than 1000?
The answer is 18.
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1 solution
Mathematica
Select[Prime@Range@PrimePi@1000,!PalindromeQ@#&&PrimeQ@IntegerReverse@#&]returns 18 pairs
here are those primes
{13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991}