# Game of primes ends as mathematics gets too difficult

By Jacob Aron An online race to solve a mathematical puzzle involving primes has ended, for now. Over the past year, mathematicians have been battling it out in a game involving primes, numbers that are only divisible by themselves and 1. Now they have called a ceasefire after the game became too difficult, but the players are tantalisingly close to proving a theory dating from 1849. The twin prime conjecture posits that there are an infinite number of pairs of primes separated by two, such as 3 and 5. In May 2013, Yitang Zhang at the University of New Hampshire in Durham made the first major progress by proving that there are an infinite number of prime pairs separated by at most 70 million. Since then, researchers have been advancing his methods to find prime pairs separated by smaller intervals. They have been working as part of the Polymath project, in which mathematicians use blogs and wikis to collaborate online. In a few weeks they had reduced the gap to just under 5 million, and today it stands at 246. In theory, the methods used could find gaps as small as six, but the researchers say they have reached a point of diminishing returns. “If we put in an enormous amount of effort, we might be able to reduce the bound a little bit further,” says Terence Tao at the University of California, Los Angeles, who has been coordinating the online efforts. “Perhaps the better thing to do is wait and see if some new idea emerges from elsewhere.” The friendly competition was a lot of fun,