# Former Subway workers makes prime number breakthrough

A previously little-known lecturer has made a significant breakthrough in the exploration of prime numbers. Dr Yitang Zhang of the University of New Hampshire has brought mathematics closer than ever before to confirming that twin primes are infinite.

A twin prime is simply two consecutive prime numbers that differ only by two. The lowest examples are three and five, five and seven, and 11 and 13. The highest known twin primes run to more than 200,000 digits.

As researchers calculate more and more prime numbers, they’ve always been able to find twin primes popping up now and again, even if they appear at wider and wider intervals. Though unproven, a widely accepted theory (the Twin Prime Conjecture) is that the number of twin primes is infinite — in other words, you can identify any twin prime you like and there’ll be one higher, even if you haven’t found it yet.

It’s a subject that interested Yitang, whose current academic posting didn’t come immediately after achieving a doctorate in 1992 — he’s said to have spent time working as an accountant and even a Subway sandwich maker while looking for a position in the US.

Last month Zitang submitted a paper on twin primes to the Annals of Mathematics, where editorial staff were so impressed they bumped it up the line for peer review. That review has now described the paper as “a landmark theorem in the distribution of prime numbers.”

The Simons Foundation has a detailed explanation of Zitang’s research and findings. He spent three years thinking about the problem, only to suddenly come up with a solution while killing time in a friend’s back yard before a night out.

The breakthrough involves the way mathematicians filter out numbers that could be primes. A 2005 technique, known as GPY, helps first identify numbers that might be part of twin primes, leaving an easier and quicker task of verifying whether this is the case in each instance.

Zitang has modified GPY in a way that means rather than just check specific numbers, he can prove a theory. In this case, he’s proven there’s an infinite number of pairs of consecutive primes that are separated by 70 million or less. That may sound incredibly vague compared to the separation of two, but the key here is providing proof.

According to Zitang, further refinement should drastically reduce the gap between primes that can be proven to repeat infinitely. However, he says it’s unlikely the system can ever prove twin primes, and instead the most likely limit is proving infinite pair separated by no more than 16.

(Picture credit: Lisa Nugent, UNH Photographic Services)