Palindromic Primes

[merlin2007]

Hi All,

Does anyone have an idea on how to determine the number of palindromic primes of a specified base and a specified digit? For example, if I asked for the number of palindromic primes with 9 digits in base 20?
This is not really a class topic, but it came up during a problem-solving discussion, and I have no idea what to do with it.

Thanks a lot.

 

[pka]

How does one define palindromic primes of a specified base ?
Please give an example in say base 5.

 

[merlin2007]

A 1-digit palindromic prime in base 5 would be the number 2_5, where x_y means x in base y.
A 3-digit palindromic prime in base 2 would be the number 101_2
A 5-digit palindromic prime in base 2 would be the number 11111_2

Whether or not a number is a palindrome depends on its representation in the given base. The number of digits is also given for that base. Whether or not a number is prime is the same regardless of base. For convenience, we could just convert everything to base 10 to test for primality.


Thanks

 

[pka]

Whether or not a number is prime is the same regardless of base. For convenience, we could just convert everything to base 10 to test for primality.

Do you understand that " to test for primality" is no simple thing, even in base 10?

 

[merlin2007]

Certainly I understand that. That is why I have no idea how to do this problem in less than exponential time.

I'm just thinking there has to be a smart way, relating to the fact that the numbers are palindromes.