# Primed Triangles

**Number Theory**Level 4

What is the sum of all prime numbers \(p\), such that \(8p+120\) is a triangle number?

**Details and assumptions**

A **triangle number** is a number of the form \( \frac {n(n+1)} {2} \), where \(n\) is a positive integer. This counts the number of dots in a triangle with \(n\) dots on a side.