A somewhat surprisingly modern thing about Pocklington's observation is that he treats all polynomials as equivalent for his purposes: > the labour required he

A somewhat surprisingly modern thing about Pocklington's observation is that he treats all polynomials as equivalent for his purposes: > the labour required here is proportional to a power of the logarithm of the modulus, not to the modulus itself or its square root as in the indirect processes, and hence see that in the case of a large modulus the direct process will be much quicker than the indirect Specifically, he's pointing out that asymptotically any power of the logarithm of n will be smaller than a constant times n. Physicists also naturally know about asymptotic comparisons, but the "this algorithm asymptotically beats that algorithm because it's (log n)^k₁ vs. k₂*n" is pretty darn similar to the way we think about this today!