The core motive of this research is to construct a new hierarchical non-DHT based architecture for Peer-to-Peer (P2P) networks that facilitate common interests clustering. DHT based network maintenance is on the high end and it churning management is a complex task here. Providing efficient data querying performance and ensuring minimal churn management effort has interested us to pursue non-DHT route of P2P networking. And at each level of the proposed architecture hierarchy, existing networks are all structured and each such network has the diameter of 1 overlay hop. Such low diameters have immense importance in designing very efficient data lookup algorithms. We shall use a mathematical model based on the Chinese Remainder Theorem (CRT), generally used in cryptography, to define the neighborhood relations among peers to obtain the above-mentioned diameters. To the best of our knowledge, use of CRT in P2P network design is a completely new idea; it does not exist in the literature so far. It is worth mentioning its most important advantage from the viewpoint of speed of communication, that is its diameter, which is only 3 overlay hops. The protocol is not restricted to a single data source, and it incorporates peer heterogeneity as well.