The Call of the Primes

I read and accepted some of Owen O’Shea’s work when I was editor of Journal of Recreational Mathematics; the response from the readership to his work was always positive. His general tactic is to start with some material that is generally known as an introduction, then “send” the material to “another” for commentary that will extend the concepts by expressing ideas based on the introduction. In this case, the “other” is Chinese number expert Dr. Cong.

The Call of the Primes is a collection of material from the world of recreational mathematics. Nearly everyone that follows recreational or popular mathematics will have no difficulty in understanding the material. Familiar topics such as magic squares, basic patterns in the prime numbers, and the most well-known conjectures about primes; the Monty Hall problem, properties of the Fibonacci and Lucas sequences; square and triangular numbers, Pascal’s Triangle as well as \(\pi\) and \(e\) are covered.

For nearly all readers, the first part of each chapter will be old and cold beans. The interesting part does not begin until Dr. Cong is heard from. Many unusual and unexpected relationships and patterns are described; this is the gold standard for recreational mathematics. Mathematicians that deal with the most abstract and complex of concepts will also find those parts a jolt to their pleasure centers as well. While I found some of Dr. Cong’s musings familiar, most were unusual enough to light a bit of a fire in me.

If you are a fan of the many ways that numbers can be related to each other and sometimes world events, then you will love the brilliance of Dr. Cong. Here is one example from the chapter on the square numbers.

Bobby Fischer won the US Championship in chess in the 1957/58 season when he was just 14 years old. He won the World Championship in chess in 1972 when he was just 29 years old. Consider those two numbers, 14 and 29. 14 multiplied by 29 equals 406. The 406th prime number is 2791. Reverse the digits of that number and one obtains 1972, the year Fischer won the World Championship.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.