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?

×