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Large sieve inequalities are a fundamental tool used to investigate prime numbers and exponential sums.ÌýIn this lecture I will explain my work that resolves aÌý1978 conjecture of S.ÌýPatterson (conditional on the Generalized Riemann hypothesis)Ìýconcerning the bias of cubic Gauss sums over the prime numbers.ÌýThis explains a well-known numerical biasÌýfirst observed by Kummer in 1846. This bias was later the subject of testing on some of the first super computers in the 20th century. Time permitting, results onÌýhigherÌýorder Gauss sums will be discussed.Ìý This isÌýjoint work with Maksym Radziwill.