What is this? Number theory? Combrinatorics?

\(x\) and \(y\) are the numbers mentioned in this problem.

Let \(b_1,b_2,\ldots ,b_{30}\) be the numbers of digits of \(a_1,a_2,\ldots,a_{30}\) respectively.

Given that the product \(a_1.a_2.....a_{30}\) has \(950x+46y\) digits and \(A^2=b_1+b_2+\cdots+b_{30}\)

What's the probability that \(A\) is a prime number?

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