We want to know how hard it is to solve a computer problem,’’ says Professor Manindra Agrawal, explaining his specialisation in computer science. It’s a skill the professor at the IIT, Kanpur, appears to have applied in zeroing in on a mathematical problem that has frustrated the best of minds .Until last week, the only thing that could definitely be said about prime numbers was that there were an infinite number of them. But now three computer scientists at IIT, Kanpur, have posted on the Internet a way for computers to determine in good time whether a number is prime or not. Says Agrawal, who led the research with two students, Neeraj Kayal and Nitin Saxena, the task they set themselves has been attempted by mathematicians for centuries. They sought to arrive at ‘‘a formula which captures all the primes.’’A prime number is one which only has two divisors: 1 and itself. To determine conclusively whether a 100-digit number is prime, it is claimed, could take more time than the age of the universe.Mathematical advances are not only rare but are put through a check by peers. For Agrawal and his students, however, endorsement has come virtually instantaneously. Shafi Goldwasser, a professor of computer science at the Massachusetts Institute of Technology whose work has been cited in Agrawal’s nine-page document, has already declared it ‘‘the best result I’ve heard in over 10 years.’’Reactions from other leading researchers have varied from the succinct ‘‘wonderful, beautiful’’ to joy that ‘‘an elegant solution has been found to such a fundamental problem.’’ Primality testing has been an abiding objective for researchers for centuries. Agrawal recalls that ‘‘mathematicians even abandoned it (the quest) as they realised that prime numbers were chaotically spread out.’’ For Agrawal, the journey began in 1998. He says a colleague, Somnath Biswas, and he were reading a paper, when Biswas proposed, let’s try to do that with primes. And so they published a paper on primality in 1999. He kept working on it . After Kayal and Saxena graduated, the trio wrote the final proof in July. Now the last lap remains, to submit it to a mathematics journal.
