prime
In traditional mathematics, an integer divisible only by 1 and itself.

Known to drive mathematicians mad searching for the next largest one - computers all over the world are continually searching. At the time of writing, the largest prime found was 12978189 digits in length.
1 is prime.
3 is prime.
7 is prime.

A joke in mathematical circles about the properties of induction goes something like:

Base case: 1 is prime
K+1 case: 3 is prime

Therefore all odd numbers are prime. QED

The joke being, of course - that due to faulty logic in the proof, the conclusion is that all odd numbers are prime - a clear fallacy (example: 21... 7*3=21 so 21 is NOT prime).