# The fun fact isn't just there for fun

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Find the number of ordered pairs of positive integers $$(a,b)$$ with $$a+b$$ prime, $$1\leq a,b \leq 3570$$ such that $$\frac{ab+1}{a+b}$$ is an integer.

Fun fact: $$3571$$ is the $$500$$ th prime number.

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