There is a light fixture in the ceiling of a high hallway in my home. You have to stand on a tall ladder to change the bulb, which is a common 100W bulb. I did this when I moved into the house in June, 1971. And even though I have used the light every day for one or two hours, I have not had to change the light since! Believe me, I would remember having carried the tall ladder up two flights of stairs and removing the fixture to do this. Why would this bulb have lasted so long? (And am I jinxing it by asking this question and thereby causing it to burn out tomorrow?)
Could be that fixture has low voltage problem. This is most likely to be caused by a relatively high resistance in the circuit path; causes of this include corroded or dirty wire nut connections and undersized wiring. In your case, it seems not be a significant problem, but remember that the energy that’s not being delivered to the bulb is causing something somewhere in the circuit to heat up. In some cases, this isn’t much of a hazard, in others, it is. I probably wouldn’t worry about it after 35 years.
The reason a lower voltage will make the bulb last an order or two of magnitude longer than its rated lifetime is because the life of a bulb is roughly proportional to the twelfth power of the applied voltage. Cutting the voltage in half, for instance, will make the bulb last approximately 4000 times as long as it would at full line voltage.
It could just be luck - distribution of failure ages is likely to resemble a bell curve - with a few of them failing after an unreasonably short life, a peak where most of them tend to fail, then tailing off with a few of them lasting a long time before dying - maybe you just got one that happens to be at the far end of the bell curve.
Nothing to add, just – wow, 35 years! And I thought I was doing good when I changed the last original light bulb in our house last month after we’d been there over ten years. (I can tell the originals because the builder used all clear glass bulbs rather than frosted.)
Where does the 12th power come from?
It’s probably an accident of manufacturing.
I worked in a plant that made sealed-beam headlamps for General Motors. Each line had its own filament winder, and the parts that handled the tungsten wire had to be replaced frequently. Tungsten is so hard that it wears out the tools that handle it. I presume this is also true of the tools that make the wire, so occasionally you get wire that’s fatter than it shoud be.
Your Methuselan light bulb probably accidentally got a sturdier filament than it was supposed to get.
Is it turned on and off frequently? Heating and cooling more often would affect the filament strength wouldn’t it?
So if I put two bulbs in a fixture in series, the romantic glow will essentially last forever. Cool.
I really have no idea. I’ve never seen the derivation of this, only the fact on its own. Perhaps one of our EE guys knows. I’d like to know the answer myself.
I don’t know but I thought that you were one of the EE guys. I know I am one of the EE guys and I have never seen this but I do IC design.
No, not quite an EE; I lack the bit of paper that says so. I can fake it pretty well, though 
Mainly what stands in my way is a poor grasp of the principles of calculus, and at my age it’s probably too late to learn. Not that I’d be much inclined to go back to school at this point, anyway. Some things truly are for the young.
As a manufacturing guy, I will add my voice to the consensus. It’s a part that’s way on the good end of the bell curve.
Nope. Tungsten is certainly harder than steel, but it’s not even close to the hardness of diamond, which is what the final drawing dies for filament wire are made of.
Setting aside the issues of abnormally low voltage, one might ask the same question about computer hard drive lifespans as well. Some drives fail 6 months to a year after purchase, some last 10 or more years.
My money is on the bell curve.
My father in law worked in a similar facility in Anderson (rhymes with Guide Lamp I think the one on Pendleton Ave.) until '98 or so. His take was that the impurities in the gas in the bulb were responsible for burnout.
It was too expensive to remove all the impurities so that is why they would blow out (unless otherwise damaged). He said when guys would appropriate their own lamps that they would blow the gas for a lot longer than production lamps removing the impurities and increasing the lamp life.
I have no idea whether this is true; it’s just related by someone that worked in a lighting facility. And I have no idea if this relates to household bulbs.
Since it is so hard to get at to replace, a previous owner, or possibly even the builder, may have had the foresight to install a long-life bulb in the fixture. These run the filament at a lower temperature, trading efficiency for long life.
The principal burnout mechanism in normal bulbs is thermal cycling, but there is also evaporation of the tungsten, that places an upper limit on lifetime.
Thomas Edison’s origional bulbs used a carbon filiment, that while delicate, had very low evaporation. There is one on a Livermore California Firehouse that has been burning since 1901 Snopes confirms it.
The OP said he installed the bulb when he first moved into the location.
It’s also a very low wattage bulb–something like 4 W, IIRC. In photos I’ve seen, the filament is glowing a dull orange-red color; probably around 1200 K or so.
Even so, the diamond dies will still eventually experience wear, won’t they? - just very slowly.
I use a lightbulb with a hole in the bulb as rudimentary oxygen detector in my inert atmosphere box so I can say there is at least some truth to this. A lightbulb that lasts this long is definitely well sealed.