TITLE: All other prime gaps (except between $2$ and $3$) are even.
QUESTION [6 upvotes]: How can one show that except for the first prime gap (between $2$ and $3$), all prime gaps are even? 
Prime gap means the difference of two consecutive primes.
For example: $5-3=2$ (even) or $17-13=4$ (even) or $23-19=4$ (even).
I have no idea how to start.

REPLY [5 votes]: All primes other than $2$ are odd, hence gap between them is even (as difference of two odd numbers is always even).