Two mathematicians were both born in the last 500 years. Each lives (or will live) to be 100 years old, then dies. Each mathematician is equally likely to be born at any point during those 500 years. What is the probability that they were contemporaries for any length of time?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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