Prime Differences

Number Theory Level 4

Let $$p_n$$ denote the $$n^\text{th}$$ prime number. For example, $$p_1 = 2, p_2 = 3, p_3=5$$.

How many pairs of positive integers $$(a,b)$$ with $$a-b \geq 2$$ are such that $$p_a - p_b$$ is a divisor of $$2(a-b)$$?

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