What is the heaviest naturally-occuring element?

Assuming you mean density, Osmium at 22600 kg/m³ is the most dense.

note that Californium at 15100 kg/m³ is less dense and is also artificial.

edit: re your added details....

wikipedia:

Plutonium is a transuranic radioactive chemical element with the symbol Pu and atomic number 94.

Plutonium is the heaviest primordial element by virtue of its most stable isotope, plutonium-244, whose half-life of about 80 million years is just long enough for the element to be found in trace quantities in nature. Plutonium is mostly a byproduct of nuclear fission in reactors where some of the neutrons released by the fission process convert uranium-238 nuclei into plutonium.

Other elements could have (probably have) existed briefly early in the formation of the earth, but have long since decayed to other elements. Heavy elements came about due to a nearby supernova burst long ago, and those elements did not exist prior to that.

Americium, #95, for example, the longest half life isotope is 243 Am, with a half life of about 7000 years, so any present earlier is now long gone.

Curium, #96, for example, the longest half life isotope is 248 Cm, with a half life of about 340000 years, so any present earlier is now long gone, after billions of years.

you can go on, but "if only briefly" is pretty vague.

Heaviest Naturally Occurring Element

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RE:

What is the heaviest naturally-occuring element?

I know that transuranic elements up to the number 118 have been synthesised in the lab, but do any of them appear naturally (if only briefly)?

Uranium is the heaviest naturally occurring element.

Californium (element number 98) is the heaviest element that has been observed in nature.

http://en.wikipedia.org/wiki/Californium

It's quite likely that at least some heavier ones do exist in nature in certain circumstances- heavy elements are produced naturally in supernovae (which is where every element heavier than iron comes from). However, these heavier elements would only occur in very low quantities and generally have a very short half-life, and so are unlikely to exist in nature.

George Bush's mom is the heaviest naturally occurring element

A pound of nitrogen weighs just as much as a pound of boron. You probably want to know the densest naturally occurring element.