Oliver and Soundararajan have recently discoveredan unexpected bias in the distribution ofprime numbers. Interestingly, the authors embarkedon this research after hearing about acounter-intuitive result obtained upon comparisonof two elementary coin tossing experiments.This article describes these experiments and presentsboth numerical and analytical methods forexploring the source of inspiration for their research.Elaboration of such key motivations orthemes provides a way of bringing the excitementof recent mathematical discoveries to theundergraduate classroom.