Generation and Primality Testing of a 4096-Digit Prime Number Using Rhythm-Based Evolutionary Density Jump Method

This study presents the generation of a 4096-digit large prime number using a rhythm-based random jump method combined with prime density evolution (Density Evolution). After generation, the number was confirmed as prime within approximately 20 seconds using the Miller-Rabin probabilistic primality test. This prime number has potential applications in cryptography and large-scale mathematical research. The complete process, including generation method, primality testing technique, digit length, and generation time, is documented.