The A580 is a mystery. It looks like an early PX4 but is marked A580 and Spec 1305. The Type designation is clearly within an M-OV etched lozenge on the envelope.
A higher gm version of the PX4? or possible a modification for an RF application are the best guesses at present.
The typical PX4 style bright anode.
The four filament hairpins held by tension springs.
The pinch and lower anode.
The classic envelope is 60 mm in diameter, and excluding the B4 base pins is 122 mm tall.