I saw some 71 watt incandescents for sale. They were
energy-saver types, but I didn't buy any. Where do they
come up with a number like 71 watts?

There are such things as 75W bulbs, so replacing one with a 71W bulb will
save you 100Wh every 25 hours of operation. If the bulb is on all the time,
you'd save about $3.50 in electricity a year.

I've seen odd numbers like that with heavy service bulbs,
and the like. Basically, they have a heavier filament.

Actually, for a given light output (notice the qualification!!!), heavy-duty
bulbs (like the 130V bulbs installed in hard-to-get-to places, such as
garage-door openers) waste energy. The lower the temperature of the
filament, the less visible light is produced. (This is covered in just about
any physics book.) But the bulb lasts longer, as the life of an incandescent
bulb varies as the 12th power (!!!) of the applied voltage.

This is why tungsten-halogen bulbs produce more light than regular
incandescents. The bulb can run hotter, because the halogen cycle (which
requires the higher temperature) returns evaporated tungsten to the
filament.

The catch is that you have to leave the bulb on for a while for this to
occur -- you can't be constantly turning it on and off. And if you use a
dimmer, you can't dim the bulb "just a bit", because you'll halt the halogen
cycle, without meaningfully lowering the filament's temperature. (I've seen
this.) To paraphrase Pope... "A little dimming is a dangerous thing. Dim
deep, or enter not the power-saving stream."