While surfing the Internet last week, I found this torrent:

2,650 year-old math problem solved by James McCanney (a.k.a. Jim McCanney). In this two hour audio file, James McCanney is interviewed by

Brad Walton (of the

WCCO radio station in Minneapolis, Minnesota, USA) about his book

Calculate Primes. It was recorded on March 17, 2007 (they wished each other a happy

Saint Patrick's Day) and Walton also

blogged about the interview on the same day.

Several of the following references that I link to are surely not reliable sources, but there are not too many references to be found, so be sure to make your own conclusion instead of just blindly believing mine.

Before I talk about the Calculate Primes, let me share what I found about McCanney himself. In the interview, Walton continually refers to McCanney as a professor, but this title misleading. McCanney's website provides

a long bio highlighting his past. The first part is about his education history, including the fact that he used be a "introductory instructor" at

Cornell University (in Ithaca, New York, USA) for the physics department and then the math department. However, he was fired from both positions for his radical theories in physics (at least according to McCanney's own bio, which I believe). In this

forum post, McCanney claims that he has also taught at other schools and "earned" the title of professor. My guess is that he is referring to schools in South America that were mentioned in his bio, which does not count in my book. So as far as mainstream academics is concerned, McCanney only reached the level of introductory instructor before being fired, twice.

McCanney has many theories in phyiscs which are not accepted by the rest of the academic community. The website Bad Astronomy has

a page dedicated to McCanney and his more "popular" theories.

Most of the hits on Google for "James McCanney" are related to his work in physics. It seems that everyone disagrees with almost all of his work. However, it is possible that his work with prime numbers is valid, so I will give McCanney's results a chance to convince me.

I was very excited to listen to the interview but also wondered why I had not heard about this before. I listened to the whole interview, but McCanney only discussed specific details about his findings a few times. From what I gathered, McCanny created some sort of function that is repeatedly applied to a set of numbers. He said that the initial set is {0, 1}. I think that the numbers in this set are added and subtracted from what McCanney called "magic numbers." Eventually McCanney said that "magic numbers" were his simplified term for sequential prime products, which are also known as

primorials. McCanney also said that this process will produce some "false primes" (some composite numbers). However, I thought he said that in the next iteration of this process, they would no longer be in the set.

In

this forum post, an owner of the book said:

"McCanney has to be the worst speller I have ever encountered. McCanney apparently does not believe in proofreading. His books have many typos and incomplete or ungrammatical sentences. Publishing material in this state is almost an insult to the reader."

The obvious lack of proofreading led me to find out who published this book. Both

McCanney's website and

Amazon had this information. Calculate Primes is self-published by "jmccanneyscience.com press."

The three hour DVD that comes with the book appears to be of the same quality. In

this forum, the eleventh poster says:

"I've looked at the DVD a bit. It's not exactly Hollywood. It appears to be essentially a home video. ...I would mention that it seems to be a low budget production."

In

this forum post, another owner of the book said:

"...Mr. McCanney changes the names of sets during the book, and sometimes uses different names for the same thing even in the same equation."

This same person goes on to say:

"The (infinite) union of repetition groups, each with an infinite number of members is effectively a sieve of Eratosthenes as far as I can see."

In agreement with this last person, the people on

this forum provided some math from McCanney's function and concluded that McCanney's work was probably a reinvention of the

Sieve of Eratosthenes. I also agree with this conclusion. Look at the numbers on the left hand side when using the "magic number" 2. They are all numbers that are not multiples of 2. When the "magic number" is 6 (= 2 x 3), the numbers on the left hand side are not multiples of 2 or 3. Finally, when the "magic number" is 30 (= 2 x 3 x 5), the numbers on the left hand side are not muliples of 2, 3, or 5.

Given the limited information that I could find on the Internet, I have concluded that McCanney's book Calculate Primes does not contain a new, revoultionary way to calculate prime numbers. In order to learn more, I would have to buy the book, but I believe that this would only cause me to be more convinced that McCanney did indeed reinvent the Sieve of Eratosthenes.