# problem with finding smallest notable number **URL:** \ **Category:** Factual Questions\ **Created:** [September 5, 2018, 8:59pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834 "2018-09-05T20:59:47Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [September 5, 2018, 8:59pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834/1 "2018-09-05T20:59:47Z")
Many months ago, a thread was started on notable numbers, asking what the smallest notable number was. Someone came in and pointed out that was an impossibility, because that number would then be notable for its least notability. There was even a theory/theorum/etc. named after someone who had studied the concept pretty thoroughly. A quick search didn’t pull anything up. Anyone have any idea what the hell I’m talking about? ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [September 5, 2018, 9:17pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834/2 "2018-09-05T21:17:04Z")
Many years ago perhaps? > **[The smallest non-interesting number](https://boards.straightdope.com/sdmb/showthread.php?t=608779)** > > There’s an argument I’ve heard which I think is fallacious. The basic idea is that numbers have various interesting properties. Two is the only even prime; three is the only prime triangular number; four is the smallest square; five is the smallest... ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [September 5, 2018, 9:20pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834/3 "2018-09-05T21:20:49Z")
It’s the notion of the smallest uninteresting number that creates a pseudo-paradox. > **[Interesting number paradox](https://en.wikipedia.org/wiki/Interesting_number_paradox)** > > The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a con "I... ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [September 5, 2018, 9:49pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834/4 "2018-09-05T21:49:01Z")
A variation of this is the [Berry Paradox](https://en.wikipedia.org/wiki/Berry_paradox). “The smallest positive integer not definable in under sixty letters” (which has 57 letters). A Google search shows no recentish mention of this by name, but Google searches of the board have been poor lately. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [September 6, 2018, 5:18pm UTC](https://boards.straightdope.com/t/problem-with-finding-smallest-notable-number/820834/5 "2018-09-06T17:18:39Z")
These are all examples of a [self reference paradox](https://en.wikipedia.org/wiki/Self-reference). Another famous one is [Russell’s Paradox](https://en.wikipedia.org/wiki/Russell%27s_paradox) in set theory.