By Natalia Kokoromyti
Christian Goldbach (1690-1764) Sometimes the most challenging problems in mathematics are the ones that can be phrased in the most seemingly simplistic way. In 1742, Prussian historian and mathematician Christian Goldbach speculated that every integer greater than 5 can be written as the sum of 3 primes, for example 21=11+7+3 (notice that a number greater than 1 is called prime, if its only positive divisors are itself and 1). After some time, Swiss mathematician Leonhard Euler formulated the strong version of the Goldbach conjecture, suspecting that all positive even integers greater than 2 can be expressed as the sum of two primes. Little did they know that two and a half centuries later, the London-based colossus in book publishing “Faber and Faber”, in an effort to boost the promotional campaign of one of its upcoming books titled “Uncle Petros and Goldbach’s Conjecture”, would offer a whopping 1 million dollars to whoever managed to prove the conjecture during the time between 20th of March 2000 to 20th of March 2002. Unfortunately no one succeeded in this daring endeavor and the conjecture remains unproven till this very day. However, in 2008, Tomás Oliveira e Silva, a researcher from the Universidade de Aveiro in Portugal, performed a distributed computer search and verified that the conjecture holds for as far as 12*10^17 (today this number has become 4*10^18). Evidently though, with this procedure we can never show that the conjecture holds for all such integers, hence mathematicians still hope for a solid proof of Goldbach’s speculation. In 1966, Chen Jing-Run, a Chinese mathematician, made significant strides forward when he proved that a sufficiently big even number can be expressed as the sum of a prime and a number that is the product of at most two primes (e.g.18=3+(3*5). Additionally, in 1995, French mathematician Olivier Ramaré showed that every even number greater than 2 is the sum of at most 6 primes. To conclude, this is where the mathematical community stands right now…but who knows what the future has in store for this much-discussed conjecture? *Definition of conjecture (From Merriam-Webster): a proposition (as in mathematics) before it has been proved or disproved.
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