Problem:
A positive integer is a palindrome if the integer obtained by reversing the sequence of digits of is equal to . The year is the only year in the current century with the following two properties:
It is a palindrome.
It factors as a product of a -digit prime palindrome and a -digit prime palindrome.
How many years in the millenium between and (including the year ) have properties and
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since a palindrome between and begins and ends with a , there are numbers, all of the form to check. Since divides , and divides and , and , these six choices can be eliminated. We then note that the remaining four numbers, and all have both required properties.
First note that is the only two-digit prime palindrome. Since , the three-digit palindrome must be less than . The only three-digit prime palindromes in this range are and . Thus, and are the only four numbers with the two required properties.