Find the Missing Digit: Complete _2 to Make a Prime Number

Question

Fill in the blank for a prime number:

2 \square2

Step-by-Step Solution

To solve the problem of finding the missing digit in 2\square2 that results in a prime number, we need to check each possible digit from 00 to 99 and see which of them make 2\square2 a prime number.

Let's perform this step-by-step analysis:

  • Step 1: Substitute 00 in place of \square, resulting in the number 0202 which should be considered as 22.
  • Step 2: Check if the number 22 is a prime number. A prime number is one that has no divisors other than 11 and itself.
  • Step 3: Determine if 22 is prime. Since 22 is divisible by only 11 and 22, it is a prime number.

Upon examining the possibilities, the use of 00 in \square results in 0202, which is equal to 22, a prime number. Therefore, the missing digit that makes 2\square2 a prime number is 00.

Thus, the correct number is 0202 or 22, and therefore the correct choice from the given options is 00.

Answer

0 0