Write all pairs of 2-digit twin primes such that on changing the places of their digits, they still remain prime numbers.

The 2-digit twin primes are: (11, 13), (17, 19), (29, 31), (41, 43), (59, 61) and (71, 73).

We check each pair by reversing the digits:

• (11, 13): Reversed → (11, 31). Both 11 and 31 are prime. ✓
• (17, 19): Reversed → (71, 91). 91 = 7 × 13, not prime. ✗
• (29, 31): Reversed → (92, 13). 92 is even, not prime. ✗
• (41, 43): Reversed → (14, 34). Both even, not prime. ✗
• (59, 61): Reversed → (95, 16). 95 = 5 × 19, 16 = 2⁴, not prime. ✗
• (71, 73): Reversed → (17, 37). Both 17 and 37 are prime. ✓

Hence, the required pairs of 2-digit twin primes are (11, 13) and (71, 73).