# Palindromic number

## Definition

"A palindromic number is a number (in some base b) that is the same when written forwards or backwards, ..."
http://mathworld.wolfram.com/PalindromicNumber.html

**THEOREM**
Theorem: There are infinitely many palindromic numbers.
Proof:
"It is fairly straightforward to appreciate (and prove) that in any base there are infinitely many palindromic numbers, since in any base the infinite sequence of numbers written (in that base) as 101, 1001, 10001, etc. (in which the nth number is a 1, followed by n zeros, followed by a 1) consists of palindromic numbers only."
https://en.wikipedia.org/wiki/Palindromic_number

Proof unavailable

**THEOREM**
"Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11."
https://en.wikipedia.org/wiki/Palindromic_prime
Theorem: Except for 11, all palindromic primes have an odd number of digits.
Proof: The divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11.

Proof unavailable

## Proper subsets