The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.

By the Sieve of Eratosthenes method find the prime numbers between 1 and 100. We find that these are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Out of these, a pair of prime numbers having same digits are 13, 31; 17, 71; 37, 73, 79, 97.