Resolution: All whole numbers are interesting.

I will be making four claims to support my argument: [C1] Proof [C2] Interesting ≠ Practicality [C3] Prime Numbers are Awesome [C4] Other Ways of Identifying and Classifying Numbers [Claim #1] Proof You can actually explicitly prove (albeit in a slightly-humorous fashion) that all whole numbers have to be interesting by using a proof by contradiction. A proof by contradiction is one where you assume the opposite of the proposition, and eventually find a contradiction, thereby proving the original proposition to hold true. The proof here is as follows: Classify all numbers as being in one of two categories: Interesting an Uninteresting My original proposition states all whole numbers are in the Interesting category, leaving the Uninteresting category empty. Assume not -> Assume that there exists at least one number that is in the Uninteresting category. -> There exists one number that would then be considered the smallest uninteresting number, thereby making the number interesting as it has a unique quality that no other uninteresting numbers possess. Therefore, that number cannot be uninteresting, and must be moved to the Interesting category. This will inevitably lead to a contradiction, as you can repeat this process for every "Uninteresting" number. ∴ The original proposition holds: All whole numbers are interesting. The crux of this argument is assuming that if a number holds a unique quality, you can (and should) classify it as interesting. Again, this is an ambiguous classification and is up to interpretation, but I am under the assumption that any reasonable person would consider a number like that to be considered "interesting". I can continue this line of logic further, but I will leave that to later rounds. [Claim #2] Interesting ≠ Practicality It would be quite difficult to say that every whole number has a practical application, and that it not what I am trying to argue. A number can be considered interesting and not necessarily have a real-world practical use. However, that also doesn't assume that we won't one day find an application for the number or its properties. For example, the number 1894 can be expressed as 14 23 32 41. Interesting? I'd think so. Practical? Maybe not in most people's lives, but that doesn't discount the fact that this property is indeed both unique and interesting to 1894. [Claim #3] Prime Numbers are Awesome A prime number is one that has exactly two factors: 1 and itself. For example, the number 3 has only itself and 1 as factors, making it prime. If a whole number (above 2) is not prime, it must be composite, meaning it has more than 2 factors. For example, 9 has exactly three factors: 1, 3, and 9. 1 and 0 are neither prime nor composite, but they are obviously already both very interesting numbers to begin with. All prime numbers can be considered interesting for two reasons: The Ulam spiral and infinity. The Ulam spiral is a visual representation of all the integers written in a spiral pattern [1]. You then highlight every prime number. When you do this to a large enough degree, you will begin to see a slight pattern to the highlighted primes. To this day, mathematicians are still perplexed as to why this happen, and there is a lot of mystery surrounding this topic and why it happens, which would then lead us to believe that prime numbers are, in fact, very interesting. There are also infinitely-many primes, which is another interesting fact. Mathematicians are constantly one-upping each other by running a computer program to try and find the next highest prime number. The last man to find the highest prime to date discovered one that was over 17 million digits long. a 17 million-digit number that has only two factors is incredibly interesting! Not only that, he's also offering a $150,000 prize for the first person to find a prime over 100 million digits long [2]. [Claim #4] Other Ways of Identifying and Classifying Numbers There are many, many other ways you can identify numbers besides just classifying them as "prime" or "composite" or "neither prime nor composite". For example, you have Mersenne primes, twin primes, sexy primes, "weird" numbers, "happy" numbers, "triangular" numbers, etc. with each one holding unique properties. With all of these crazy classifications, I would argue the BoP is on Con to show which numbers can be considered "uninteresting" and why. I look foward to hearing your response Con. Source(s): [1] . http://www.ulamspiral.com... [2] . http://www.dailymail.co.uk...