12 can be made into a prime by changing the 2 to 3; likewise, 63 can be changed into a prime by changing the 6 to 7.

What is the smallest number that cannot changed into a prime by changing a single digit?

Are there infinitely many such numbers?

200. To change the number into a prime number, the last digit must be changed. Otherwise, it will end in 0 and not be prime. Changing the 0 of 200 to an even digit will make it even. Changing the 0 to 5 will make it divisible by 5. Therefore, we must change the 0 to 1, 3, 7, or 9. However, 201=3*67, 203=7*29, 207=3*3*29, and 209=11*19. Therefore, there is no way to change a digit of 200 to get a prime.

Posted by Math Man on 2024-12-11 15:33:18