A proof by H. Iwaniec in 'On the problem of Jacobsthal, Demonstratio Math. 11, 225–231, (1978)' shows that: $$j(N) \ll \log^2 (N)$$
where $j(N)$ is the Jacobsthal function.
I am very interested in understanding the details of this proof.
Would anyone be able to provide a rough outline of the proof and suggest a good reference for understanding the theory behind Iwaniec's argument?
Edit: I changed the expression based on feedback. $\log \log N$ was incorrect so I am changing it to $\log^2(N)$