With recent developments in ad hoc networks and sensor networks, random-access protocol without feedback is a technique that deserves a closer look. This paper is based on Massey's model on random-access channel without feedback. A central concept of this model is the idea of protocol sequences. For these sequences, it is desirable that their cross correlation should be as low as possible and that the length of their period should not be too long, even if there is a large number of active users. Another useful feature is to be able to support multirate communication. Based on these considerations, a new family of protocol sequences is proposed in this paper. These new protocol sequences are built on the concept of prime sequences. It is shown that these sequences possess properties that make them suitable candidates for designing random access protocols for certain ad hoc or sensor networks