Apologies for the formatting, I'm not well-versed in math and I'm unfamiliar with the styles used here. I was wondering, is there any arithmetic sequence with at least three terms and a common difference of one that the sum is prime? I've been doodling on a white board trying to figure this out, I appreciate any reply or hint in the right direction!
Edit: I shouldn't of left it to be implied, but the arithmetic progression should only consist of natural numbers!
$$ a + (a+1) + (a+2) + \cdots + (a+n) = \frac{(n+1)(a+b)}{2} $$ so it won't be prime.
(To see that, write the sum in reverse order and add term by term.)
(But good for you for doodling around with mathematics.)