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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