The thread on that screw is: .1656dia x 37tpi.
A classic "Enfield Special".
Not something they stock at the corner hardware shop; ditto the taps and dies.
And think of all the fun you can have shuffling the extra gears for your lathe gearbox to set it up for 37 TPI. Bear in mind that 37 TPI has a pitch of 0.686486486486mm, which is VERY close to 0.7mm. You can easily do that on a metric lathe. (M4 has a pitch of 0.7mm). Interestingly, the nominal diameter works out to 4.20624mm. Hmmmmm....
However, if you have a tame CNC shop nearby, and the like a challenge, you have the technology. The operator simply plugs in a CORRECTLY ground thread-form tool (NOT 60 degree), "tells' the machine what pitch and diameter are required at the correct stage and the machine does its thing. Think: infinitely variable ratio drives. Unless your friendly CNC shop is VERY tame, one screw will cost an arm and a leg. However, a hundred is just a couple of key-strokes away and wildly cheaper per unit. Keep a few for future projects and offer the rest for a reasonably sane price on the "for-sale" pages here. A win for everybody.
I've been down that track getting screws and other dinky bits made for the Francotte-actioned BSA Martini Cadet rifles. Still steadily selling off the "extras", which, in turn, has put me in contact with some interesting folk and THEIR projects / problems.