A Spectral Method for Ultra-Fast Generation of Large Prime Numbers

Key Points

• The aim is to develop ultra-fast algorithms for generating large prime numbers, crucial for cryptography.
• Developed two algorithms: a deterministic one for locating prime clusters and a randomized one using Riemann's explicit formula.
• Measured generation times for 1024-bit and 2048-bit prime numbers.
• Achieved 100% accuracy compared to conventional methods.
• Mean generation time of 16.97 ms for 1024-bit primes and 284 ms for 2048-bit primes.
• Both algorithms significantly outperform traditional prime generation methods.