Chennai born mathematician Kannan Soundararajan and his colleague Robert Lemke Oliver from Stanford University, USA, have found a strange pattern in prime numbers; that is they are not distributed as randomly as it was assumed.
Every time you make an online purchase with a credit card, prime numbers spring into action to complete the transaction for you securely. The researchers have stumbled upon a new phenomenon. In their study published on arXiv, show that consecutive prime numbers try hard not to be similar. This study has stumped mathematicians the world over.
Will this new found phenomenon have any impact on online transaction? A. Ragu Raman catches up with Kannan Soundararajan about his Chennai connections and research.
Q About your Chennai connections…
I grew up in Chennai doing my schooling in Padma Seshadri (Nungambakkam) from 1986-1991. During this time, my school teachers thought that I was talented in mathematics, and introduced me to Alladi Ramakrishnan who had founded the Institute for Mathematical Sciences (at Taramani). Through him I found out about this Institute and had the privilege of meeting Prof. R. Balasubramanian there (who recently retired as Director of the Institute). Prof. Balasubramanian had a huge impact on my development .
Q Since when were you fascinated with maths? Who is your favourite mathematician?
I’ve been fascinated in mathematics since my school years. One influential factor was the Ramanujan centenary year in 1987, which led to a lot of visibility for mathematics. Apart from Ramanujan, I am very motivated by the work of many great mathematicians from the past such as Riemann, and many contemporary mathematicians.
Q What is your area of research and what are you trying to achieve in maths?
My area of research in mathematics is number theory. This includes problems involving prime numbers, which is the topic of my recent work with Lemke Oliver. It also includes objects called zeta and L-functions, which encode much information about numbers, and understanding these functions has been the main goal of my research.
Q What prompted you to particularly look for this phenomenon in prime numbers?
I was motivated by a lecture by a colleague Tadashi Tokieda on “Rock, paper, scissors in probability.” I began wondering if there were some related phenomena in the primes, and this led to my work with my colleague Robert Lemke Oliver.
Q Your study says prime numbers are not as random as we have known?
What we found was a strange feature in the distribution of prime numbers: if a prime ends in a particular digit, then the next prime seems to dislike ending in that same digit. This is a special case of a more general phenomenon for which we give a full explanation. It subsequently turned out that a couple of other mathematicians had also found the phenomenon, but we have been the first to explain it and predict what happens when the primes get larger and larger. The explanation we found is based on a well established set of conjectures in number theory known as Hardy-Littlewood conjectures.
Q What were the first reactions from mathematicians to your finding?
Our colleagues have been very excited by the findings. We gave a talk on this at a recent conference in honor of Prof. Krishnaswami Alladi (son of Alladi Ramakrishnan) and many people were intrigued and excited by the work.
Q How big a challenge is it to explain the phenomenon?
While we were optimistic that we would be able to use these conjectures to explain our phenomena, there was still some hard work involved to figure out exactly how the mechanism worked.
Q Does it have any practical implication on rules of cryptography that plays a major role in our important online transactions?
The main interest in our work is the unexpectedness and novelty of the phenomenon. It is unlikely to have any practical applications to cryptography or encryption.
Q What kind of impact the findings will have in maths research?
As for the impact on research into primes, it is not clear what the eventual impact will be. There will be more work into understanding other contexts in which such phenomena occur, and about how widespread it is. At the moment all we can say is that it is surprising and it is unclear where it leads.