Excel and the Goldbach Comet

This article shows ways in which Excel can be used to explore the Goldbach Conjecture. We first show an elementary approach in which the Goldbach Comet is constructed by means of a table of values. Second, we give two simple VBA programs that generate substantially more data for the Goldbach Comet. We then show how the Comet can be seen as the agglomeration of individual bands and use that approach to suggest an improvement to the Hardy‐ Littlewood formula for the number of ways in which an even number can be expressed as the sum of two primes. We also outline two further investigations into the form of the Goldbach Comet. After expanding the comet to show exactly which prime pairs make a given even number, conditional formatting is used to elucidate patterns in those pairings, and we also explore the possibility that Goldbach’s conjecture might still hold even when the number of primes used is greatly reduced. Throughout, the focus is on ways in which Excel can be used to process and display very large amounts of data and on the underlying patterns that emerge when it is used in this way.