In many scientific communities using experiment databases, one of the crucial problems is how to assess the statistical significance (p-value) of a discovered hypothesis. Especially, combinatorial hypothesis assessment is a hard problem because it requires a multiple-testing procedure with a very large factor of the p-value correction. Recently, Terada et al. proposed a novel method of the p-value correction, called "Limitless Arity Multiple-testing Procedure" (LAMP), which is based on frequent itemset enumeration to exclude meaninglessly infrequent itemsets which will never be significant. The LAMP makes much more accurate p-value correction than previous method, and it empowers the scientific discovery. However, the original LAMP implementation is sometimes too time-consuming for practical databases. We propose a new LAMP algorithm that essentially executes itemset mining algorithm once, while the previous one executes many times. Our experimental results show that the proposed method is much (10 to 100 times) faster than the original LAMP. This algorithm enables us to discover significant p-value patterns in quite short time even for very large-scale databases. © 2014 Springer-Verlag.