Primed Triangles

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.

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