Factoring may be easier than we think (2016)

Enough people have tried to find efficient factoring algorithms that we can be confident the problem isn’t easy, but there’s no reason to think it’s impossible. These functions interpolate between L (n) = nc and L (n) = (log n)c.

Until the 1970’s, the best algorithms known for factoring all had running times of the form L (n) for some constant c. Some people suspected that this was the true complexity of factoring, but in the late 1980’s the number field sieve reduced the running time to L (n).

Source: math.mit.edu