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"Prime conjecture verified to new heights," by Ivars Peterson. Science News, 12 August 2000, page 103.
Can every even number be written as the sum of two prime numbers? Christian Goldbach believed so, spurring 250 years of incredible mathematical innovation, but as of yet, no proof. Researcher Jorg Richstein, of the Institute of Informatics at the University of Giessen in Germany, continues the trend. By reformulating an existing algorithm, Richstein applied modest computer power to verify the Goldbach conjecture for even numbers up to 4 times 1014---previous computations had verified it for even numbers up to 1014---and to calculate the number of ways each even number up to 5 times 108 can be written as the sum of two primes. He found that the larger the number, the more distinct ways there are to write it as a sum of two primes. For instance, only two pairs of distinct primes add up to 20, while 291,400 distinct pairs add up to 100 million. His results strengthen the doubt that a larger even number will provide a counterexample to Goldbach's claim. In the meantime, a British publisher's offer of a US$1 million prize for a proof of the Goldbach conjecture may stimulate researchers to answer the question once and for all.
--- Kathryn Leonard
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