
The name of the book perfectly describes the obsession of some mathematicians. ‘Primes’ are such a group of special numbers. On surface, it doesn’t look like there is a rule of predicting primes and their distribution, but on the other hand, there appears to be a pattern, a regularity of their appearance among all the infinite numbers. But if we only treat primes simply as an object of obsession of some weird scholars, we would be terribly wrong, because prime numbers are the basis for many encryption systems we are using nowadays.
This book aims to explain the “Riemann hypothesis”, a hypothesis about the distribution of primes, to the general readers who are interested in mathematics. Riemann hypothesis is proposed by a German mathematician Bernhard Riemann in 1859. So far, even after 150 years, mathematicians still cannot refute or confirm it. It is a fascinating story.
In the course of reading the book, I was side-tracked by the mentioning of the ‘sieve of Eratosthenes’. It is a method developed by an ancient Greek mathematician, Eratosthenes of Cyrene, more than 2200 years ago to derive primes. At the first look, I thought the method is quite interesting, but on the second look, I found out it is nothing but remove the multiples one by one from the lowest numbers. Say we want to find out the prime numbers between 1 and 100. All we have to do is to remove all the numbers that contain a lower number (other than 1) as their factor. For example, we start from 2, and remove all the numbers with 2 as a factor, such as 4, 6, 8, etc, and then we move to 3, and remove all the numbers with 3 as factor, such as 9, 15, 21, etc. After continuing to do so, all the numbers left will be prime numbers.

I thought the name of Eratosthenes sounds familiar. After consulting the wikipedia, I found out he was also famous for accurately measured the earth’s circumference, which is a story I read before. He had been busy indeed. One thing I didn’t realize is that, Wikipedia also mentions that Eratosthenes’ contemporaries gave him a nickname of ‘beta’, from the second letter of the Greek alphabet, because he was considered as the second best in the world in almost any field. I am sure this is meant to be an honor, but something it just doesn’t feel right.