First off nice recovery but unless you are putting a centre hole in a shaft for running in the lathe forget centre drills.

I know most books and tomes of learning tell you to centre drill first but all these were written years ago before CNC. Industry hardy ever uses centre drills now, they use spotting drills very short fluted and stiff drills with a different angle on them and it's well worth buying a couple of the smaller sizes to replace centre drills.

If you do need to centre drill then it also pays to regrind the drill and loose half the pilot length, they are far too long to do what they need to achieve.
years ago it was to form a reservoir for the white lead that lubricated the dead centre. Nowadays most people use a revolting centre and this doesn't apply. All the pilot has to do is stop the point touching the end and this can also be achieved by having a small flat on the very nose of the revolving centre, this also protects the centre to a degree as if it doesn't have a sharp point it can't get damaged.

Now someone will say grinding the pilot down will loose half it's life, but snapping it will loose all it's life, make the choice.

JS.