2017 is not just another prime number (opens in new tab)

Proof is by contradiction: Assume that not every number is mathematically interesting and let X be the first such number. However, the fact that X is the lowest such number is itself pretty special, right?

   All throughout the talk there were statements like "Let p be an odd prime and…"
   
   My friend asked, “what is an odd prime?”—thinking it must be special in some way. The answer back was: not 2.

Someone thought to check how often there is a number and that number plus 2 that are both prime, and there seems to be a pattern there, which is the twin primes conjecture [1]. Along the way, a lot of other places are investigated in this search for patterns, such as the sum of the cube of gap primes that the grandparent mentions.

Recording investigations made along these lines is often done by recording it in the Online Encyclopedia of Integer Sequences [2]. (Significant findings merit publication in journals.)

The end result is that one can perform a search for a particular number and see in which sequences it appears. This is how the linked post came to be.

[1] https://en.wikipedia.org/wiki/Twin_prime#Conjectures [2] oeis.org