Saturday, August 15, 2009

Highly Palindromic Primes

Over at the μtoast the blogger Attila Oláh described an in interesting property of primes in Highly palindromic primes.

In his post Atilla explores the question "How palindromic is a prime number?". For a prime \(p\) he inspects all the representations in meaningful bases i.e. all bases from 1 to \(p-1\). Attila then counts the number of representations which are palindromes.

In the search for higly palindromic primes, Atilla lists 291721. It is a prime number which is palindromic in 16 bases. I found several highly palindromic primes which are palindromes in 17 bases, and one prime which is a palindrome in 18 bases.

The primes I found which are palindromes in 17 bases are: 950041, 960961, 1062601, 1108801. The prime which is a palindrome in 18 bases is: 1259701.

Which higly palindromic primes can you find?

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