You Can Count on Monsters
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You Can Count on Monsters is a children's book
which presents the concepts of prime numbers and factoring
in a novel and colorful way. The book is based on a
poster I made.

The book starts with a 20 page introduction, written
at an elementary school level. After explaining multiplication,
prime numbers, and factoring, the introduction lays out the
general idea for the rest of the book, as I'll now describe.
To each prime number, we associate a pattern of dots
and a monster. Examples:

There is something about each monster that has to do with the prime.
Part of the fun of the book is figuring out how the monster is related to its prime.
For each composite number, we factor the number into primes
and then draw a scene that involves the corresponding monsters. We also show
an arrangement of dots and a factoring tree that helps explain
the picture. (A factoring tree is a kind of diagram that
shows one way to factor the number into primes.) Examples:

The end of the book has two short appendices. The first
appendix explains the Sieve of Eratosthenes , an ancient method
for generating the primes. The second appendix gives a liesurely
account of Euclid's famous proof that there exist infinitely many primes.