Interesting number paradox

The interesting number paradox states that all natural numbers are interesting.

The proof goes like this: Assume there were uninteresting numbers at all. Then, in the set of uninteresting numbers, there would be a smallest one. But this number would then be interesting for the property of being the smallest uninteresting number. This contradiction shows that the set of uninteresting numbers must be empty.

Some have attempted to find this "smallest uninteresting number" anyway. The smallest number not in OEIS, the Online Encyclopedia of Integer Sequences, is currently 17843. The smallest number which does not have its own Wikipedia article is 262. And the smallest number that has no special properties listed anywhere in Wikipedia except for a prime factorization is 275.