A San Jose State University professor who announced just weeks ago that he and a colleague had solved an important math problem now says he goofed.

Daniel Goldston had worked on the problem for 20 years.

"Even if I had spent another year very carefully going over everything, I think I still would have missed that error," Goldston said Tuesday.

Goldston's advance in the field of prime numbers was called the most important breakthrough in that area of mathematics in decades.

Other experts say that regardless of the outcome, the work Goldston has done with Cem Yalcin Yildirim of Bogazici University in Istanbul is a success.

Goldston's work involves the twin prime conjecture, or the idea that there are an infinite number of pairs of prime numbers that differ only by two.

Prime numbers can be divided only by themselves or by 1 without leaving a remainder. The smallest twin primes are 3 and 5. The largest discovered so far are numbers with 51,090 digits each.

While no one has proved the twin prime conjecture itself, Goldston and Yikdirim tackled a related question: Can you find an infinite number of primes that may not be twins, but that are much closer together than average?

Their proof, or solution, seemed to say yes. But on April 23, a flaw emerged.

Goldston says he will work to fix the flaw over the next several months - mostly at his dining table, while his wife and three children watch television.