The number p is the product of three different positive prime numbers greater than 2.If the sum of these three prime number is also prime, what is the smallest possible value for p?
Won't the 3 number be 3-5-11?
Thanks
Yes, that would add to give you the smallest prime p.
To find the smallest possible value for p, we need to consider the prime numbers greater than 2 and see if any combination satisfies the given conditions.
Let's start by finding three prime numbers greater than 2. The prime numbers greater than 2 are 3, 5, 7, 11, 13, 17, 19, etc.
Now, let's calculate the sum of the three primes and check if the sum is also a prime number.
Taking the first three primes, 3, 5, and 7, their sum is 3 + 5 + 7 = 15. However, 15 is not a prime number (it is divisible by 3 and 5).
Next, let's consider the next combination, 5, 7, and 11. The sum of these three primes is 5 + 7 + 11 = 23. And indeed, 23 is a prime number.
Therefore, the smallest possible value for p, which is the product of these three primes, is p = 5 * 7 * 11 = 385.
So, you are correct. The smallest possible value for p is 385 when the three primes are 5, 7, and 11.
To find the smallest possible value for p, let's analyze the problem.
We know that p is the product of three different positive prime numbers greater than 2. The smallest prime number greater than 2 is 3. So, let's start with that.
Now, the sum of these three prime numbers should also be prime. Therefore, we need to find three primes whose sum is prime.
Starting with 3, we can add the next prime number, which is 5. The sum of these two primes is 3 + 5 = 8, which is not prime.
Since 8 is not prime, we need to go to the next prime number, which is 7. Now, if we add 3, 5, and 7, we get 3 + 5 + 7 = 15, which is also not prime.
We need to continue this process until we find three primes whose sum is prime. The next prime number after 7 is 11. If we add 3, 5, and 11, we get 3 + 5 + 11 = 19, which is a prime number.
Therefore, the correct answer is 3 * 5 * 11 = 165. So, the smallest possible value for p is 165.
So, the numbers 3, 5, and 11 are indeed three different positive prime numbers greater than 2, and their product is 165, as you correctly stated.