Cracking Goldbach’s Conjecture

How High-Throughput Compute helped mathematicians to tackle an old problem

Goldbach’s Conjecture says that every even number larger than four is the sum of two odd prime numbers, for example 6 = 3+3, 8 = 3+5, 60 = 43+17, and so on.

Christian Goldbach first proposed this in 1742, in a letter to Swiss mathematician Leonhard Euler and it sounds easy enough to understand. Unfortunately, it’s not easy to prove and Goldbach’s Conjecture remains firmly on the ‘to do’ list of mathematical challenges to crack.

Tomás Oliveira e Silva, from the University of Aveiro in Portugal turned his attention to the verification of Goldbach’s Conjecture in 2001, with the help of an ad hoc group of mathematics enthusiasts from all over the world. One of them is Silvio Pardi, a computer scientist who works at the WLCG Tier-2 site in INFN-Napoli and who brought grid computing onboard.

Silvio adapted Tomás’s code to run in an HTC environment and thanks to the HTC resources provided by the Italian Grid Infrastructure, Silvio was able to speed up the verification procedure considerably: he increased the rate in such a way that they were able to do what would take almost 2 to 3 years in only 4 months.

Although the problem of Goldbach’s Conjecture remains unproven, these verification efforts are an interesting empirical result that may one day be part of a proof. And for the near future Tomás is planning to continue his research with the help of high-throughput compute.

HTC could help mathematicians solve a 200-year-old problem, first described in a 1742 letter from Christian Goldbach to Leonhard Euler.