The sum of more than two consecutive natural numbers cannot be prime.
Is the statement true and is there any way to prove it?
I was able to prove that the sum of an odd amount of consecutive numbers cannot be prime:
So, since the sum of consecutive integers is $x+(x+1)+(x+2)+(x+3)$ etc... we can also write this as $$nx + n(n-1)/2 = n(x + (n-1)/2)$$ with $n$ as the amount of numbers and $x$ the first number in the row. So, with an odd number as $n\neq 1$, we will get a product which will never result in a prime.
Any way to prove this for all $n \ge 2$? Thanks for all the help.