In this study we used how discrete mathematics can be used to make blockchain technology safer and more reliable in this paper. Foundational ideas from number theory and graph theory are used to model and study bitcoin networks and crypto primitives. We look into how discrete mathematics tools let us evaluate agreement methods in great detail to make sure they are trustworthy and can handle mistakes in this paper. In order to make sure that the blockchain is more reliable, experts are also looking into some aspects of cryptographic hash functions. The goal of this paper is to present a complete method for improving the efficiency and safety of blockchain systems by combining several mathematical models.