If it was exponential to log N then the exp and the log would cancel. It's exponential to a sublinear function (cube root) of log N, not log N. https://en.wiki

If it was exponential to log N then the exp and the log would cancel. It's exponential to a sublinear function (cube root) of log N, not log N. https://en.wikipedia.org/wiki/General_number_field_sieve https://en.wikipedia.org/wiki/General_number_field_sieve > The running time of the number field sieve is super-polynomial but sub-exponential in the size of the input.