# Prime Problem (reposted)

Let $$n$$ denote the product of the first 2013 primes. Find the sum of all primes $$p$$ (for $$20<p<150$$) such that

• $$\dfrac{p+1}{2}$$ is even but is not a power of 2.

• there exist pairwise distinct positive integers $$a,b,c$$ for which $a^n(a-b)(a-c) + b^n(b-c)(b-a) + c^n(c-a)(c-b)$ is divisible by $$p$$, but not by $$p^2$$.

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