23

This number is a prime.

There are 23 essentially different ways to color the nine squares of a 3-by-3 checkerboard, such that 5 of the squares are black, and 4 are red. Z = RED, O = BLACK:

 
   OZO   OZO        ZOO   ZZO   ZZO   ZZO   ZOO   ZOO
   ZOZ   ZZZ        ZZZ   ZZO   OZZ   ZOZ   ZOZ   OZZ
   OZO   OOO        OOO   OOO   OOO   OOO   OZO   OZO

 ZZZ   ZZZ   ZZZ  ZZO  ZZO  ZZO  ZZO  ZOZ  ZOO  OOZ  ZOZ
 ZOO   OZO   OOO  OOO  OOO  OOZ  ZOO  ZZO  ZZO  ZZO  ZOO
 OOO   OOO   OZO  ZZO  OZZ  OOZ  OOZ  OOO  OOZ  OOZ  OZO

          ZZZ   ZOZ   ZOZ          ZOZ
          OOO   ZOO   OZO          OOO
          ZOO   OOZ   OOZ          ZOZ

[Green]