A positive interger N is a palindrome if the interger obtained by reversing the sequence of digits of N is equal to N. The year 1991 is the year with the following two properties: it is a palindrome and it factors as a product of a two-digit prime palindrome and a three-digit palindrome and a three digit palindrome.
Find all years in the milleniom between 1000 and 2000 hat has the same properties.
We know that all the 4 digit palindromes are divisible by 11 so that can be our 2 digit prime number. Since the other factor is a 3 digit, we can only look be looking at palindromes between 1100 and 2000. With that information we can easily say thatthe last digit of the 3 digit number is 1. The 3 digit numbers: 101, 111...,181, we find that there are 4 3 digit prime numbers. We know this because when we multiply by 11 we get palindromes.