The number of two digit prime numbers, with distinct digits, on being reversed they give again the prime number is :

Options

A. 3
B. 5
C. 8
D. 11

Answer

To solve the question of finding the number of two-digit prime numbers with distinct digits that, when reversed, also yield a prime number, we can follow these steps:

### Step 1: Identify Two-Digit Prime Numbers
First, we need to list all the two-digit prime numbers. The two-digit prime numbers are:
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

### Step 2: Filter for Distinct Digits
Next, we need to filter out the prime numbers that have distinct digits. The prime numbers with distinct digits are:
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Note: We exclude 11 because it has repeated digits.

### Step 3: Reverse the Numbers
Now, we will reverse each of these prime numbers and check if the reversed number is also a prime number:
- 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 Valid Pairs
From our checks, the valid two-digit prime numbers with distinct digits that remain prime when reversed are:
- 13 and 31
- 17 and 71
- 37 and 73
- 79 and 97

Thus, we have a total of **4 pairs**: (13, 31), (17, 71), (37, 73), and (79, 97).

### Final Answer
The number of two-digit prime numbers with distinct digits that, when reversed, also yield a prime number is **4**.

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