Mostly right, but only for light skin (and depends on the month and the latitude) (Table 1, Table 3). Dark skin usually needs 10-15 minutes (Table 2), and even 20 minutes for the darkest skin (Table 4). https://doi.org/10.3390/nu16101489
I read the summary thoroughly and scanned the rest, and I don’t think the paper supports the grandparent comment.
The paper says you can produce enough vitamin d to maintain healthy levels from a specific amount of sunlight per day, depending on latitude and skin color.
The original comment suggests that there’s some (very short!) limit beyond which the body is unable to produce more vitamin d, which is very different. I’d be very curious to see sources for that.
UVB synthesizes cholecalciferol (vitamin D3) in the skin, which the liver converts into calcifediol (what blood tests usually measure), which the kidneys convert to calcitriol (the active hormone). Wiki claims the kidneys have a negative feedback loop, converting excess calcifediol into inactive 24,25-dihydroxycholecalciferol. I wish I had better sources (for my vitamin D pdf folder).
The same wiki article says there is a limit to the capacity of synthesis by UVB due to the quantity of reagent 7-dehydrocholesterol produced in the skin, but I don't know the math on what amount of exposure would be required to hit that limit - presumably it (or something like it) is covered in the article above.
Some napkin math, then. About 25–50 μg 7-DHC / cm2 skin (Wiki). About 1.5 m^2 human skin area (google AI summary). About 35% skin exposed (R. Kift, linked earlier). 1.5 * 100 * 100 * 25 * .35 = 131250 μg. Need 50-250 μg of colecalciferol (2000-10000 IU). Anyone would likely get sunburn before running out of 7-DHC (excepting a low 7-DHC condition, or me getting the wrong numbers).
This study says "Findings include that small UV doses on a regular basis are more efficient for vitamin D synthesis than larger sub-erythemal doses", using a logarithmic model for blood calcifediol as a function of exposure.
But it doesn't address colecalciferol production and storage. Fat stores colecalciferol, and I don't know of any way to measure that directly. I would guess that further UVB exposure linearly produces colecalciferol (with linear DNA damage, minus DNA repair with time), but the liver and kidneys logarithmically produce calcifediol and calcitriol. Just a guess. Still more questions :)
All i know is that i feel miserable if i dont get sunlight for extended periods (months) and i feel fantastic (again) after 20-30 minutes of shirt-less sun exposure. It's not the heat, it lasts for days.
The cold doesnt bother me, i sunbath in the winter too. This obviously isnt for everyone.
Even if it is bad for me i dont need anyones help. Let them go shut down Burger King and Jack Daniels and whatever enjoyable bad things people do.