I am the prime next to Optimus

Algebra Level 2

On the line given by

\(3x +8y =143\) ,

there are exactly 2 points \(\text{(a,b)}\) and \(\text{(c,c)}\) such that \(\text{a,b,c} \in \mathbb{Z}^+\) and \(a,b,c\) are prime numbers.

Find the value \(a+b+c\)

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