Problem

Source: 2024 Argentina L2 P6

Tags: number theory



A list of $7$ numbers is constructed using the following procedure: each number in the list is equal to the sum of the previous number and the previous number written in reverse order. For example, if a number in the list is $23544$, the next number is $68076 = 23544 + 44532$. (It is forbidden for any number in the list to start with $0$, although the reversed numbers may start with $0$.) Decide whether it is possible to choose the first number of the list so that the seventh number is a prime number.