1. **Problem statement:** We need to find a whole number $n$ such that the product $n \times (n + 42)$ is a prime number. 2. **Recall the definition of a prime number:** A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 3. **Analyze the product:** The expression is $n(n + 42)$, which is a product of two integers. 4. **Important rule:** For a product of two integers to be prime, one of the integers must be 1 or -1, because if both factors are greater than 1 or less than -1, the product will have more than two divisors. 5. **Check possible values:** - If $n = 1$, then $n(n + 42) = 1 \times 43 = 43$, which is prime. - If $n = -43$, then $n(n + 42) = -43 \times (-1) = 43$, also prime, but $n$ must be a whole number (usually non-negative integers), so we discard negative values. 6. **Conclusion:** The only whole number $n$ that makes $n(n + 42)$ prime is $n = 1$, and the prime number is $43$. **Final answer:** $43$