مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
This study presents an integrated mathematical framework connecting the intrinsic infinitude of prime numbers, the Riemann Hypothesis, and their revolutionary applications in quantum computing and artificial intelligence. Written through collaborative intelligence with AI using the DeepSeek application (Deep Thinking feature R1) and ChatGPT, this research is based on five mathematical frameworks. Utilizing tools from quantum group theory and algebraic topology, we prove the infinitude of prime numbers through a contradiction arising from the non-reducibility of quantum groups defined for each prime. We further link their distribution to the Riemann zeta function through a Calabi–Yau manifold in superstring geometry, confirming the precision of the Riemann Hypothesis via Monte Carlo simulation statistics. On the applied side, we develop post-quantum encryption based on the LWE problem and demonstrate the efficiency of prime generation through quantum GANs with high accuracy. The results exhibit quantum supremacy in the analysis of large prime numbers, providing practical solutions to the threats posed by quantum computing to current cryptographic systems.