The introduction of blockchain technology has brought about significant transformation in the realm of digital transactions, providing a secure and transparent platform for peer-to-peer interactions that cannot be tampered with. The decentralised and distributed nature of blockchains guarantees the integrity and authenticity of the data, eliminating the need for intermediaries. The applications of this technology are not limited to the financial sector, but extend to various areas, such as supply chain management, identity verification, and governance. At the core of these blockchains is the consensus mechanism, which plays a crucial role in ensuring the reliability and integrity of a system. Consensus mechanisms are essential for achieving an agreement amongst network participants regarding the validity of transactions and the order in which they are recorded on the blockchain. By incorporating consensus mechanisms, blockchains ensure that all honest nodes in the network reach a consensus on whether to accept or reject a block, based on predefined rules and criteria. The aim of this study is to introduce a novel consensus mechanism named Erdos, which seeks to address the shortcomings of existing consensus algorithms, such as the Proof of Work and Proof of Stake. Erdos emphasises security, decentralisation, and fairness. One notable feature of this mechanism is its equitable node-selection algorithm, which ensures equal opportunities for all nodes to engage in block creation and validation. In addition, Erdos implements a deterministic block finalisation process that guarantees the integrity and authenticity of the blockchain. The main contribution of this research lies in its innovative approach to deterministic block finalisation, which effectively mitigates the various security risks associated with blockchain systems.