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As soon as one tries to combine the primes and the otherfundamental operation of arithmetic, namely addition, oneswiftly comes up with questions that have provedimpossible to answer.Most famous amongst these is Goldbach’s Conjecture,which hypothesises that every even number is the sum oftwo primes. Given a smallish even number it is easy tocheck that it is the sum of two primes, for example 104 = 31+ 73. To a mathematician, of course, checking that everyeven number less than 100,000,000 is a sum of two primesis not good enough, and we demand a proof thatGoldbach’s Conjecture holds for all numbers. Such a proofis currently lacking and most experts do not expectdefinitive progress on the problem in the near future.There is a weaker version of Goldbach’s Conjecture,which has been proven. Namely, it is known that everysufficiently large odd number is the sum of three primenumbers. Cambridge mathematicians G. H. Hardy and J. E.Littlewood were the first to plot a path to a proof of thisresult. It is known that “sufficiently large” in this contextcan be taken to mean greater than 10^43001. This is a numberso large that it is of mathematical, rather than merelycomputational, interest to show that every odd number isthe sum of three primes.