I am the prime next to Optimus

Algebra Level 2

On the line given by

3x+8y=1433x +8y =143 ,

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

Find the value a+b+ca+b+c

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