As the size of a semiprime increases, the number of smooth numbers that can be discovered (the "yield") by the GNFS with polynomials selected with academically

As the size of a semiprime increases, the number of smooth numbers that can be discovered (the "yield") by the GNFS with polynomials selected with academically known optimal polynomial selection algorithms decreases. With a reduction in smooth candidates the GNFS sieve operation can be wholly unsuccessful. If a smooth barrier exists (such as a semiprime size where smooth yield becomes deficient) factoring time degenerates from the GNFS improved rate to old school factoring rates due to the need to pivot. Yield decay has been observed <2048bit. If 2048bit is easily factorable for the NSA, no barrier challenge is suggested.