The number of two digit prime number which remain prime even on inverting the position of its digits is :

Options

A. 4
B. 5
C. 9
D. 10

Answer

To solve the problem of finding the number of two-digit prime numbers that remain prime even when the digits are inverted, we can follow these steps:

### Step 1: Identify all 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: Invert the digits of each two-digit prime number
Now we will invert the digits of each of these prime numbers and check if the resulting number is 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 3: Count the valid two-digit prime numbers
Now we will list the two-digit prime numbers that remain prime when their digits are inverted:
- 11
- 13
- 17
- 31
- 37
- 71
- 73
- 79
- 97

### Step 4: Total the count
Counting the valid numbers gives us a total of 9 two-digit prime numbers that remain prime when their digits are inverted.

### Final Answer
The number of two-digit prime numbers which remain prime even on inverting the position of their digits is **9**.

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