TITLE: Probability that a number and its digit reversal are relatively prime
QUESTION [7 upvotes]: What is the probability that a number and its digit reversal are relatively prime in base b?

REPLY [3 votes]: I think there are bases $b$ where the probability becomes arbitrarily low. Let $b$ be the product of the first $n$ primes plus one then the difference of $b$ and its palindrome will be divisible by $b-1$ and for them to be relatively prime neither can be divided by the first $n$ primes. So if $n$ is chosen large enough the probability can be made arbitrarily low.