How many increasing sequences of three distinct prime numbers have a sum of 20?

Answer 1

List the primes up to 20 (2, 3, 5, 7, 11, 13, 17, 19) and note that the largest possible prime in the sum is 13 because no two primes add up to and of course 19 is too large as well. Also, observe that 2, the only even prime, must be in the sum, because the sum of three odd primes cannot never be 20. Starting with 2 and 3, we see that is not prime. Next, 2 and 5 give , a prime, so one such increasing sequence is 2, 5, 13. Next, we take 2 and 7, and we see that is prime as well, giving us the second sequence 2, 7, 11. 11 and 13 are already included, so we are done. Thus, there are increasing sequences of three distinct prime numbers that have a sum of 20.

Answer 2

To find the number of increasing sequences of three distinct prime numbers that sum up to 20, we can start by listing out the prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, and 19. Since the sequence must be increasing, the first Prime number can only be 2, as it is the smallest prime. We can then set up an equation for the remaining two prime numbers: 2 + x + y = 20, where x and y are the other two prime numbers. By trial and error, we find that the only solution is 2 + 7 + 11 = 20. Therefore, there is only one increasing sequence of three distinct prime numbers that sum up to 20, which is {2, 7, 11}.

Answer 3

Oh, what a happy little question! Let's paint a picture with numbers. We start by finding the prime numbers that add up to 20. There's only one way: 3, 7, and 10. Remember, in math and in art, there are no mistakes, just happy little accidents.

Answer 4

Oh, dude, let me break it down for you. So, the only way to make 20 with three distinct prime numbers is 3, 7, and 10. But, technically, 3, 7, 10 is not increasing because 3 is less than 7. So, the answer is zero. Like, sorry, but no increasing sequences of three distinct prime numbers add up to 20.