Entropy-Based Adaptive Sieve Optimization in Classical Number Theory

This work introduces an entropy-based adaptive sieve that selectively removes multiples of primes to minimize local gap irregularity among survivors. In contrast to the traditional Sieve of Eratosthenes, which removes all multiples indiscriminately, the adaptive sieve maintains smoother number distributions and preserves more survivors. The approach suggests new strategies for prime filtration, randomness control, and number-theoretic structure analysis.