Dirichlet's theorem on arithmetic progressions states that for any two positive integers a and b, if gcd(a,b) = 1 then the arithmetic progression t(n) = a*n + b (n ≥ 0) contains inﬁnitely many prime numbers. Recall that a prime number is a positive integer ≥ 2 that has no divisors other than 1 and itself. For example, if a = 4 and b = 3, then the arithmetic progression is  3, 7, 11, 15, 19, 23, 27, 31, 35, ..., and it can be seen that many prime numbers are contained in the ﬁrst part of this list. Given arbitrary integers a > 0, b ≥ 0, and U ≥ L ≥ 0, your job is to count how many values of t(n) = a*n+b are prime, where L ≤ n ≤ U.