The year 2002 is a palindrome because it does not change when read from right to left.

373 and 1221

were palindromic years.

(a) What will be the next palindromic year after 2002?

(b) The last palindromic year, 1991, was odd. When will the next odd palindromic year be?

(c) The last prime palindromic year occurred more than 1000 years ago, in 929. When will the next prime palindromic year occur?
(a) The next one is 2112.

(b) The next odd palindrome is 3003.

(c) To be prime, the palindrome cannot have four digits, as every four-digit palindrome is of the form $a b b a$, which is divisible by 11, since

$$
\begin{aligned}
a b b a & =a 00 a+b b 0=a \times 1001+b \times 110=a \times 11 \times 91+b \times 11 \times 10 \\
& =(91 a+10 b) \times 11
\end{aligned}
$$

The first five-digit palindrome is $10001=73 \times 137$, which is not prime. The next possible candidates are

$$
10101=3367 \times 3 \text { and } 10201=101 \times 101
$$

Thus, the first palindrome prime after 929 is 10301.