Which of the following is NOT a prime number?

### Concept & Logic To verify if a number $N$ is prime, you do not need to test every number up to $N$. You only need to find the approximate square root of $N$, denoted as $\sqrt{N}$. Test for divisibility only by the prime numbers less than or equal to this square root. If it is not divisible by any of them, it is prime. ### Step-by-Step Solution * **Test Option A (241):** The square root is slightly less than 16 (since $16^2 = 256$). Prime numbers below 16 are 2, 3, 5, 7, 11, 13. 241 is not divisible by any of these. Thus, 241 is prime. * **Test Option B (337):** The square root is less than 19 (since $19^2 = 361$). Primes below 19 are 2, 3, 5, 7, 11, 13, 17. 337 is not divisible by any of these. Thus, 337 is prime. * **Test Option C (391):** The square root is less than 20 (since $20^2 = 400$). Primes below 20 are 2, 3, 5, 7, 11, 13, 17, 19. * Testing divisibility for 391: It fails for 2, 3, 5, 7, 11, and 13. * Let's test 17: $391 \div 17 = 23$. * Since 391 is evenly divisible by 17, it has factors other than 1 and itself. Therefore, 391 is NOT a prime number. ### Exam Strategy & Shortcut Use divisibility rules for 2, 3, 5, and 11 first to quickly eliminate obvious numbers. When testing larger primes like 13, 17, or 19, look at the unit digit. For example, to get a unit digit of 1 in 391 using the prime 17, you need to multiply 7 by a number ending in 3 (like 13 or 23). $17 \times 20 = 340$, and $17 \times 3 = 51$. $340 + 51 = 391$. ### Common Pitfall A massive time-waster is trying to divide a large number by every single odd number sequentially. Always stop checking once your prime divisor exceeds the approximate square root of the target number. ### Final Answer Therefore, the correct answer is **391**.