Forget Sudoku, Try This Puzzler

Mathematicians have taken a giant step towards cracking one of the oldest and most complex number puzzles - without a Sudoku grid in sight.

The puzzle, known as the twin prime conjecture, has stumped the best mathematical brains for centuries.

Of similar status to Fermat's last theorem, it even appeared as the subject of a chat-up line in the 1996 Hollywood film The Mirror Has Two Faces. Now, number experts Dan Goldston of San Jose State University in California and Cem Yildrim of Bogazici University in Istanbul, working with Janos Pintz of the Hungarian Academy of Sciences, have paved the way for a solution. Prof Goldston announced the breakthrough at the American Institute of Mathematics in Palo Alto, California.

Brian Conrey, director of the institute, said: "A couple of months ago I would have told anybody who asked that no one has ever had a plausible idea for proving the twin prime conjecture. Today, I think it is feasible that it will be resolved in the next few years."

The twin prime conjecture proposes there are an infinite number of paired prime numbers that differ only by two, such as 3 and 5, 11 and 13, 29 and 31. But as the size of the prime numbers soars, so does the difficulty of keeping track of them. The trio's work does not prove that huge prime numbers also crop up in pairs, but it suggests they are likely to, based on an analysis of the average size of the gap between them. In effect, they have paved the way for the full solution of the riddle.

Marcus du Sautoy, a mathematician at Oxford University, said: "This is one of those problems that, if you can prove, you will write your name in mathematics history. A lot of these things are very simple to state, but incredibly difficult to prove."