Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2025 / Paper 1 / 1 / b / Solution

It performs a trial division test for a prime number. An integer below $2$ is rejected; otherwise the function searches for a divisor from $2$ through $\lfloor \sqrt{n}\rfloor$. A composite number has a prime factor no larger than its square root, so finding no such divisor proves primality. For example, mystery2(97) returns True, while mystery2(91) returns False, since $91=7\cdot 13$.

This describes the intended mathematical test. For extremely large integers, the floating-point computation n**0.5 can round or overflow; an implementation intended for arbitrary-size integers should use an exact integer square root.