I run the specalized armadilo (not the light) range of tyres on my road bike and mountain (and soon to be electric bike).
Never had a puncture since i converted to them. this includes riding over broken glass etc. They are more heavy than a normal tyre, but have kevlar belts to stop punctures.
Nails are bad tho - there are not a lot of tyres that will stop a nail if it hits in the right place - ie the sidewall. ( i realise urs hit dead center - this may have been ok).
just look for something that has a kevlar bead in it, but my preference is the specalised all condition armadilo (23x700c for road bike)
and the armadilo slick tyre (forget the model) 1.5 x 26" for mountain