What are Palindrome Numbers?
They are numbers that read the same forward or backward. Single digit numbers qualify (1,2,3,4,5,6,7,8, and 9), as do the 11 times tables through 9 (11,22,33,44,55,66,77,88, and 99). The smallest three digit palindrome is 101. The first interesting property of palindrome numbers is that all palindrome numbers with an even number of digits are divisible by 11. Two digit numbers are obvious, but what about four digit numbers? The first four digit palindrome is 1001 which is divisible by 11. The next four digit palindrome is 1111, which is also divisible by 11 and is 110 bigger than 1001. 110 is important, because not only is it divisible by 11, but every four digit palindrome is x(1001) + y(110), where x is any integer from 1 to 9, and y is any integer from 0 to 9. Since 11 is a factor of both 1001 and 110, then all four digit primes are divisible by 11, and since 11 is the only common prime factor of 1001 (prime factors 7, 11, 13) and 110 (prime factors 2, 5, 11), it is the only number
