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
answer by K Sengupta)
The required smallest number that cannot be made into a prime ny changing a single digit is 200.
--> Changing its hundreds digit will always make the resultant number divisible by 100. Contradiction.
--> Changing its tens digit will always leave the resultant number divisible by 10.
Therefore, the digit change must occur corresponding to its unit digit.
Obviously, changing the 0 to any other even number, will make the resultant number even, and therefore composite.
The last digit cannot be changed to 5, as any number ending with 5 must be divisible by 5.
Now, we observe that:
201=3*67. Contradiction.
203= 7*29. Contradiction.
207 = 9*23. Contradiction.
209= 11*19. Contradiction.
Consequently, the required smallest number is 200
Explanation to answer for part (a)
