What if I think that all of the numbers are uninteresting? Does that make them all interesting? But doesn't that, in turn, make all of them uninteresting?
Assume that some numbers are not interesting. Let n be the smallest non-interesting number. Since n is the smallest number that's not interesting, it is interesting.
You may think you're a Trekkie, but did you know that the first Star Trek parody show was a one season flop called "Quark?" It was about an interstellar garbage scow, and it had a crew including two clones.
So, I picked it by choosing 12^3 + 2. I wanted to start with something easily factored (power of 12) and not too small, but not interesting because of its factorization. And I wanted it to be even, since odd numbers tend to have funny quirks. So a simple +2.
What's amusing is that I did this before looking at the Wikipedia page. According to that, the original number that inspired this paradox was 1729. So just by happenstance, I picked one integer higher than the original "uninteresting" number. Which I guess arguably makes 1730 interesting now (though admittedly not for mathematical reasons).
the interestingness of numbers is a field that fulfills Laplace's equation, with the constraint that 0 is infinitely interesting, and the interestingness converges to zero for n -> infinity.