In this paper, we study the missing patterns problem: Find the shortest pair of patterns that do not occur close to each other in a given text, i.e., the distance between their occurrences is always greater than a given threshold α. We present various solutions to this problem, as well as to the case where the patterns in the pair are required to be of the same length. This work is motivated by optimizing the sensitivity of PCR. Experiments show that our algorithm is practical enough to handle human genome data.