User blog comment:Primussupremus/Primus Notation part 2./@comment-27516045-20170225151829

Not that much improvement.

n(n)-n-n is equal to (n^^n)^^(n^^n). THis is roughly equal to n^^n^^n or n(n(n)).

A better improvement would be to make a function that does n(n(...)) for m times.