Take the first n prime numbers, 2, 3, 5, …, p n , and divide them into two groups in any way whatever. Find the product of the numbers in each group, and call these A and B. (If one of the groups is empty, assign it the product 1.) No matter how the numbers are grouped, and will always turn out to be prime numbers, provided only that they’re less than (and greater than 1, of course). For example, here’s what we get for (2, 3, 5) (where = 72 = 49):

2 × 3 + 5 = 11

2 × 5 + 3 = 13

2 × 5 – 3 = 7

3 × 5 + 2 = 17

3 × 5 – 2 = 13

2 × 3 × 5 + 1 = 31

2 × 3 × 5 – 1 = 29

In More Mathematical Morsels (1991), Ross Honsberger writes, “For me, the fascination with this procedure seems to lie to a considerable extent in the amusement of watching it actually turn out prime numbers; I’m sure I only half believed it would work until I had seen it performed a few times.”