Divisibility information by small primes cannot by itself reliably distinguish integers with an odd or even total number of prime factors. Consequently an upper-bound Selberg sieve can bound prime pairs and related sifted sets but does not supply a positive lower bound or the conjectured twin-prime asymptotic. This limitation concerns the information available to the sieve, not merely a choice of weight normalization.
// Target: number-theory.bigb
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