Isn't that wonderful. All those years we spent in the car together when she was a child learning to be aware of the math around us really is paying off as she negotiates her way through her 30th year.
My mission in life as a math educator is to help young children become aware of the mathematical relationships around them; the mathematical patterns, numerical relationships, relative sizes and places of things; where there are circles, squares, perpendiculars and parallels, unknowns that can be found through problem solving and the aesthetics of it all. Prine numbers are a classic example of how unthinking, rote learned classroom math can destroy our sense of mathematical wonderment. Remember the wonderful definition and test for prime numbers that we all learned? "A prime number is a number that is divisible only by one and itself". A search of the Internet will reveal a whole variety of definitions each more complicated than the next.
To young children first coming into contact with the concept (about 3rd grade) we need something that illustrates the concept of the prime number visually, efficiently, meaningfully, and clearly. This can be achieved by using the area or array concept of multiplication. Every multiplication fact makes either a rectangle, series of rectangles or a square: 4 makes a 1 x 4 or a 2 x 2: 9 makes a 1 x 9 or a 3 x 3 square (hence its name - square number): 7 makes only a 1 x 7 rectangle, 13 makes only a 1 x 13 rectangle and 23 makes only a 1 x 23 rectangle. So prime numbers make only one rectangle - unlike 24 which makes a 1 x 24, 2 x 12, 3 x 8, and 4 x 6 rectangles.