To solve this, we identify all two-digit prime numbers, reverse their digits, and check if the resulting number is also prime. Here's the step-by-step process:

Step 1: List of Two-Digit Prime Numbers

Two-digit primes are: $11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.$

Step 2: Reverse the Digits

Reversing the digits of each prime number gives:

• 11 → 11
• 13 → 31
• 17 → 71
• 19 → 91
• 23 → 32
• 29 → 92
• 31 → 13
• 37 → 73
• 41 → 14
• 43 → 34
• 47 → 74
• 53 → 35
• 59 → 95
• 61 → 16
• 67 → 76
• 71 → 17
• 73 → 37
• 79 → 97
• 83 → 38
• 89 → 98
• 97 → 79

Step 3: Check Which Reversed Numbers Are Prime

From the above list, we check which reversed numbers are also prime:

• 11 → 11 (prime)
• 13 → 31 (prime)
• 17 → 71 (prime)
• 19 → 91 (not prime)
• 23 → 32 (not prime)
• 29 → 92 (not prime)
• 31 → 13 (prime)
• 37 → 73 (prime)
• 41 → 14 (not prime)
• 43 → 34 (not prime)
• 47 → 74 (not prime)
• 53 → 35 (not prime)
• 59 → 95 (not prime)
• 61 → 16 (not prime)
• 67 → 76 (not prime)
• 71 → 17 (prime)
• 73 → 37 (prime)
• 79 → 97 (prime)
• 83 → 38 (not prime)
• 89 → 98 (not prime)
• 97 → 79 (prime)

Step 4: Count the Two-Digit Primes That Remain Prime

The primes that remain prime after reversal are: $11, 13, 17, 31, 37, 71, 73, 79, 97.$

Thus, there are 9 two-digit primes that remain prime when their digits are reversed.

---

Would you like a detailed explanation of how prime numbers were verified? Here are 5 related questions for deeper exploration:

1. What are the methods to verify if a number is prime?
2. How do you determine prime numbers in a specific range efficiently?
3. What are palindromic primes, and how are they related to this problem?
4. Can this process be automated using a programming algorithm?
5. What other number properties remain invariant under digit reversal?

Tip: Reversing digits can be a useful tool for exploring numerical properties, especially in problems involving symmetry or