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.
In their study published on arXiv, they have tried to 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 research.
Since when were you fascinated with maths?
I’ve been fascinated in mathematics since schooldays. One influential factor was the Ramanujan centenary 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 such as Riemann, etc.
What is your area of research and what are you trying to achieve?
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.
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.
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.
How did other mathematicians react 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.
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 the phenomenon there was still some work involved to figure out exactly how the mechanism worked.
Does it have any practical implication?
The main interest in our work is the novelty of the phenomenon. It is unlikely to have any practical applications to cryptography.
What is a prime number?
A clear rule determines exactly what makes a prime: it’s a whole number that can’t be exactly divided by anything except 1 and itself. But there’s no recognisable pattern in the occurrence of the prime.
