Question 38
Start with some positive integer. The following operation is performed on the number: its unit digit is split off and multiplied by $4$, then this product is added to the remaining number. (For example, $1997$ is changed to $7 \times 4 + 199 = 227$.) The operation is performed again and again. Prove that if the sequence of numbers obtained contains $1001$, then none of the numbers in the sequence can be a prime number.