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Uncovering a prime failure

Mathematicians have returned to the drawing board after what looked like a dramatic step forward in understanding prime numbers–those whole numbers divisible only by themselves and 1. Daniel A. Goldston of San Jose (Calif.) State University and Cem Y. Yildirim of Bogazii University in Istanbul have acknowledged a flaw in work they announced in March, which appeared to say that tight clusters of primes show up among whole numbers no matter how large the numbers are (SN: 3/29/03, p. 195: Prime Finding: Mathematicians mind the gap).

For more than a century, mathematicians have speculated that there are infinitely many pairs of "twin" primes, such as 11 and 13, which differ only by two. Goldston and Yildirim had created much excitement among number theorists when it appeared that they had come much closer to proving the twin-prime conjecture than others had managed to do in previous attempts.

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