# Primes in AP

Number Theory Level pending

Find all triplets of the form $$p_1,n,p_2$$ where $$p_1,p_2$$ are Twin primes and $$n$$, their arithmetic mean is a Triangular number.

Enter your answer as sum of the solutions $$\sum (p_i+n_i+p_{2i})$$ .

Explicit example : Say if you've got the solutions as $$(1,2,3)$$ and $$(29,30,31)$$ then your answer would be $$1+2+3+29+30+31=96$$

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