Theorem: There are no uninteresting natural numbers.
Proof: Notice that the first several natural numbers have interesting properties.  0 is the additive identity; 1 is the multiplicative identity; 2 is the first prime; 3 is the first odd prime; 4 is the first composite number; 5 is the first number which is the sum of two different primes, and so on.  So, suppose by contradiction that there are uninteresting natural numbers.  Let U be the set of uninteresting natural numbers; as a subset of the natural numbers, by the Well-Ordering Principle, U has a least element n.  But the smallest element of a set is by definition interesting, so n cannot exist.  Thus, U cannot exist, and all natural numbers are interesting.