For numbers that can be arranged by size, this can be proved. Suppose that some numbers are not interesting. The set of such boring numbers can, as agreed, be arranged by size, so one of the dull numbers is the smallest member of the set. But that makes it a number of interest, since it is the smallest number known that has no unusual properties. This contradicts the premise that all the numbers in this set are without interest, so such a set must not exist.
All numbers are interesting.
Taking a field guide-like approach, it offers a fresh way of looking at individual numbers and the properties that make them unique, which are also the properties essential for mental computation. The result provides new insights into mathematical patterns and relationships and an increased appreciation for the sheer wonder of numbers. Thus 28, the next perfect number, is a similar species. And the fact that 6 can easily be broken into 2 and 3 is part of its personality, a trait that is helpful when large numbers are being either multiplied or divided by 6. Associations with 6 include its relationship to the radius of a circle.