A residual network trained on primes up to 10^9 learns probabilistic filters for seven prime families that generalize to 10^16 and recover the correct Hardy-Littlewood asymptotic directions without explicit density supervision.
Exploring prime number classification: achieving high recall rate and rapid convergence with sparse encoding
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Neural Prime Sieves: Density-Driven Generalization and Empirical Evidence for Hardy-Littlewood Asymptotics
A residual network trained on primes up to 10^9 learns probabilistic filters for seven prime families that generalize to 10^16 and recover the correct Hardy-Littlewood asymptotic directions without explicit density supervision.