Complete the Number: Finding Prime Numbers Ending in 1

To solve the problem, we will follow these steps:

• Step 1: List down the potential numbers we can form: 11, 51, 81, and 91.
• Step 2: Identify prime numbers by testing divisibility.

Let's analyze each number:

11: The only divisors of 11 are 1 and 11 itself, which makes it a prime number.

51: Check divisibility: 51 is divisible by 3, thus it is not prime because 51 ÷ 3 = 17.

81: Check divisibility: 81 is divisible by 3 (since 8+1=9, which is divisible by 3). So, 81 ÷ 3 = 27, and it is not a prime.

91: Check divisibility further: 91 is divisible by 7 (as 91 ÷ 7 = 13) which makes it not prime.

After examining each option, 11 is the only prime number.

Therefore, the solution to the problem is $11$.