Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Prime conjecture verified to new heights," by Ivars Peterson. ScienceNews, 12 August 2000, page 103.

Can every even number be written as the sum of two prime numbers? ChristianGoldbach believed so, spurring 250 years of incredible mathematical innovation,but as of yet, no proof. Researcher Jorg Richstein, of the Institute ofInformatics at the University of Giessen in Germany, continues the trend. Byreformulating an existing algorithm, Richstein applied modest computer power toverify the Goldbach conjecture for even numbers up to 4 times1014---previous computations had verified it for even numbers up to1014---and to calculate the number of ways each even number up to 5times 108 can be written as the sum of two primes. He found that thelarger the number, the more distinct ways there are to write it as a sum of twoprimes. For instance, only two pairs of distinct primes add up to 20, while291,400 distinct pairs add up to 100 million. His results strengthen the doubtthat a larger even number will provide a counterexample to Goldbach's claim. Inthe meantime, a British publisher's offer of a US$1 million prize for a proof ofthe Goldbach conjecture may stimulate researchers to answer the question onceand for all.

--- Kathryn Leonard

American Mathematical Society