Explanation

• 997 is a prime number, while 996, 998, and 999 are not.
  • 996 is divisible by 2, 3, 6, 12, ..., and is therefore not prime.
  • 998 is divisible by 2, 7, 14, ..., and is therefore not prime.
  • 999 is divisible by 3, 9, 27, ..., and is therefore not prime.

• So, the greatest 3-digit prime is 997.