Prime Differences

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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