Question 17
A positive integer $N$ is a palindrome if the integer obtained by reversing the sequence of digits of $N$ is equal to $N.$ The year $1991$ is the only year in the current century with the following two properties:
(a) It is a palindrome.
(b) It factors as a product of a $2$-digit prime palindrome and a $3$-digit prime palindrome.
How many years in the millennium between $1000$ and $2000$ (including the year $1991$) have properties (a) and (b)?
(a) It is a palindrome.
(b) It factors as a product of a $2$-digit prime palindrome and a $3$-digit prime palindrome.
How many years in the millennium between $1000$ and $2000$ (including the year $1991$) have properties (a) and (b)?