The positive number n is the product of three different prime numbers greater than 2. If the sum of these three prime numbers is also prime, what is the smallest possible value for n?
What is a prime number? A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
I personally encourage students to memorize the prime numbers less than 100, at least less than 30.
See the following chart:
Because we are asking to find the smallest possible value for n, normally we start from the smallest prime numbers greater that 2. Let's first consider, 3, 5 and 7. The sum of these three prime numbers is 15, which is not a prime number, so 3, 5, 7 are not satisfied. We drop 7 and and consider 11 because we still want to keep the n as small as possible. Now we have 3, 5 and 11. The sum of these three numbers is 19. Check the chart above, YAHOO! 19 is a prime number. Then, we know n = 3*5*11 = 165 is the smallest possible value for n.
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