It is generally believed that data mining results do not violate the anonymity of the individuals recorded in the source database. In fact, data mining models and patterns, in order to ensure a required statistical significance, represent a large number of individuals and thus conceal individual identities: this is the case of the minimum support threshold in association rule mining. In this paper we show that this belief is ill-founded. By shifting the concept of k-anonymity from data to patterns, we formally characterize the notion of a threat to anonymity in the context of pattern discovery, and provide a methodology to efficiently and effectively identify all possible such threats that might arise from the disclosure of a set of extracted patterns.