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?
(In reply to re: Another thought - A simple solution for the 2nd part
If you add eleven, you would be changing TWO digits at the same time.