Dr. Chris K. Caldwell, UTM math professor, recently had mathematical research published in the Journal of Integer Sequences.

The work was published in the August edition of the online journal and was titled “Determining Mills Constant and a Note on Honaker’s Problem.”

“I did this research because a mathematician called and wanted to know how I knew that my number for Mills constant was correct. I couldn’t give him an answer. I realized that many mathematicians had the same answer that I did, but none of us knew why it was correct. So, I decided to do the research to find out,” says Caldwell.

The research stretched from 2002 to 2005. The first step to Caldwell’s research was to define prime numbers, which are numbers only divisible by one and themselves. For example, prime factors of 10 are two and five. Mills proved that there is a number a such that the integer part of a raised to the three raised to the nth power is prime for all integers n. Caldwell then showed that given the right assumption, that you can calculate a.

He calculated a to 6,000 decimals places.

Though Caldwell did much of the research himself, he did seek some help from fellow mathematician Yuanyou Cheng.

After doing the research, he submitted the article to the Journal of Integer Sequences, where it was reviewed by “referees”, asking questions, such as, “It is correct?” and “Is it appropriate for our journal?” The answer was yes.

Currently, Caldwell is working on other research dealing with prime numbers and their distribution. He has had around 20 articles published and one book published in Japanese titled The Encyclopedia of Prime Numbers. He also has created over 5,000 websites dealing with the same material.

A palindrome is a word or a number that reads the same in both directions, such as the word “mom.” Palindromic prime pyramids meet both criteria.

A palindromic prime pyramid uses the number above it as the base for the row below it.

The idea of studying palindromic prime pyramids began with research by G.L. Honaker in Bristol, Va.

Currently, both Caldwell and Honaker are working to build the pyramids higher.

Caldwell enjoys his position here at UTM. He says that the most fulfilling thing about his job is when students achieve, what math teachers call the “aha moment.”

“It’s that moment when the light bulb seems to finally go off, and they get it. That’s what I love,” says Caldwell.

Caldwell received his Ph.D. from the University of California at Berkeley in algebraic number theory.