Sequence mining is one of the fundamental data mining tasks. In this paper we present a novel approach called PRISM, for mining frequent sequences. PRISM utilizes a vertical approach for enumeration and support counting, based on the novel notion of prime block encoding, which in turn is based on prime factorization theory. Via an extensive evaluation on both synthetic and real datasets, we show that PRISM outperforms popular sequence mining methods like SPADE [10], PrefixSpan [6] and SPAM [2], by an order of magnitude or more.