I want to light a normal LED for as long as possible on two AA or AAA batteries. It does not have to blink or so, just stay on. The LED doesn't have to light at the max, as long as it's visible from ~1 meter.
The LED is designed for 2.5V/16mA, however, 1.9V/0.25mA is also still possible. Below that, I don't get enough light from it anymore.
I might not be looking for the fewest power consuming circuit, as some other circuits might work at a lower voltage as well. For example, consider a circuit drawing 20mA for >2V and a circuit drawing 25mA for >1V, then the second would be a better option.
What would be the circuit to give the longest lifetime?
Size is not an issue, nor is manufacturing cost or amount of components. You can use a microcontroller if you want, however, an Arduino would be a dealbreaker.