This work introduces MAX (Mathematical Applied to eXcryption), an innovative cryptographic algorithm that rapidly generates large prime numbers from random values of hundreds of digits. The algorithm uses these prime numbers to derive secure cryptographic keys characterized by a short lifespan, enhancing security and reducing vulnerability to attacks. Key generation is based on derived parameters, such as the quantity and common prefix of the found primes, ensuring efficient encryption even in environments with high latency or unstable connections. MAX is highly adaptable: parameters such as the length of the initial value and the number of iterations can be customized based on the available computing power, allowing for the generation of larger prime numbers and enhanced security. With the advent of quantum computers, short-lived temporary keys represent a strategic advantage against future attacks. The proposed implementation is designed to easily integrate into existing systems, ensuring robustness, scalability, and resilience. Note on the Updated Version: This version of the document includes references to a new publication dedicated to the applications of the MAX algorithm in the Internet of Things (IoT). The new publication explores how MAX can be used to autonomously generate cryptographic keys on synchronized IoT devices, enhancing security and eliminating the need for key transmission. For more details, please refer to the specific work: "Application of the MAX Algorithm for Secure Autonomous Cryptographic Key Generation in the Internet of Things (IoT)," available at the following DOI: https://doi.org/10.5281/zenodo.14173672