[samf]

Some examples are in these comments, e.g. the Fundamental Theorem of Arithmetic. The Sieve of Eratosthenes is an amusing outcome, where 1 is the only prime if you take it literally.

But also mentioned elsewhere in the thread: if we declared 1 to be a prime, then many (I daresay "most") of our theorems would have to change "prime number" to "prime number greater than one".

[dullcrisp]

If you defined 1 to be a prime but to not be odd then some theorems could stay the same.

[samf]

Ha, yes, I was thinking of the theorems that refer to "odd prime" to exclude 2. :-)