The sum of 7 consecutive natural numbers is 1617. Find how many of these are prime numbers?

Question: The sum of 7 consecutive natural numbers is 1617. Find how many of these are prime numbers?

Solution:
Let the first number of the 7 consecutive natural numbers is x.
Then the seven numbers are,
x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6

Their sum is,
7x + (0 + 1 + 2 + 3 + 4 + 5 + 6) = 1617
⇒ 7x + 21 = 1617
⇒ 7x = 1617 - 21 = 1596
⇒ x = 1596/7
∴ x = 228

So the seven consecutive numbers are 228, 229, 230, 231, 232, 233, 234

Now, check which are prime.
228 ; even - not prime
229 ; Prime
230 ; even - not prime
231 ; divisible by 3 (2 + 3 + 1 = 6) - not prime
232 ; even - not prime
233 ; Prime
234 ; even - not prime

So Prime numbers: 229 and 233

So, there are 2 prime numbers.