Find the number of primes that are 8 digit palindromes.
I got this question in a entrance paper. The only thing I know is the definition of a palindrome.
Also, is there any method/formula to count or approximate the first $n$ palindromes?
elementary-number-theorypalindromeprime numbers
Find the number of primes that are 8 digit palindromes.
I got this question in a entrance paper. The only thing I know is the definition of a palindrome.
Also, is there any method/formula to count or approximate the first $n$ palindromes?
Best Answer
Summarizing the hints and clarifications made in comments above:
One of the properties of prime numbers is that they cannot be divisible by any other number other than itself and $1$.
A palindrome is a number (or string) which is read the same forwards as backwards. These can be of odd length like your example of $12321$ but they can also be of even length $12344321$.
The divisibility test for $11$ should work wonders here if you can pay attention how to apply it.
Having used the divisibility test for $11$ will point out a crucial observation about any palindromic 8-digit number which will imply something about whether or not it can be prime.