Mathematicians Make Leap in Solving Age-Old Proof

Theory on infinite pairs of 'twin primes' closer to resolution
By John Johnson,  Newser Staff
Posted May 14, 2013 3:22 PM CDT

(Newser) – If you're the type to get into bar bets about prime numbers, we have exciting news. Mathematicians have taken a big step toward solving one of the oldest math problems on record, one involving "twin primes," reports Nature. The upshot is that they're closer to stating definitively that an infinite number of twin primes exists—that is, one prime separated in value from the next prime by a value of 2. (The easiest example of twin primes is 3 and 5, but the list from the showoffs at i09 also includes 2,003,663,613×2195,000−1 and 2,003,663,613×2195,000+1.)

The new breakthrough from the University of New Hampshire's Zhang Yitang does not, in fact, prove that an infinite number of primes that differ in value from their nearest neighbor by 2 exists. Zhang's figure? Seventy million. But that's still a huge deal in math circles, because he established an upper boundary for the long-held conjecture. It's a "step toward the ultimate answer," says an expert at San Jose State University not involved with the work. "His result is beautiful," says another at Rutgers. Or as New Scientist puts it, "prime numbers just got less lonely."

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