Paul kgyy wrote:
I guess it's time to really get to work on that fission reactor for my
PA28. But if everybody did that, the supply of yellowcake would
probably run out too.

Yup - used up in only a few million years - so it's a waste of time! :-)

Seriously though, the supply of uranium on earth could probably supply
all of humanity's energy needs for millions of years even at per capita
consumption an order of magnitude greater than today.

In the November 2004 "Physics Today" magazine Bernard L. Cohen stated:

"The world's energy needs could be provided by uranium-fueled breeder
reactors for the full billion years that life on Earth will be
sustainable, without the price of electricity increasing by more than a
small fraction of 1% due to raw fuel costs[1]....

The cost of extracting uranium from its most plentiful source, seawater,
is about $250 per pound—the energy equivalent of gasoline at 0.13 cent
per gallon! The uranium now in the oceans could provide the world's
current electricity usage for 7 million years. But seawater uranium
levels are constantly being replenished, by rivers that carry uranium
dissolved out of rock, at a rate sufficient to provide 20 times the
world's current total electricity usage. In view of the geological cycles
of erosion, subduction, and land uplift, this process could continue for
a billion years with no appreciable reduction of the uranium
concentration in seawater and hence no increase in extraction costs."

Here's the letters section, online:
http://www.physicstoday.org/vol-57/iss-11/p12.html

[1] 1. B. L. Cohen, Am. J. Phys. 51, 75 (1983).

And here's a report on an experiment actually carried out on extracting
yellowcake from seawater:

"Aquaculture of Uranium in Seawater by a Fabric-Adsorbent Submerged
System"
http://www.ans.org/pubs/journals/nt/va-144-2-274-278 :

"The total amount of uranium dissolved in seawater at a uniform
concentration of 3 mg U/m3 in the world's oceans is 4.5 billion tons. An
adsorption method using polymeric adsorbents capable of specifically
recovering uranium from seawater is reported to be economically feasible.
A uranium-specific nonwoven fabric was used as the adsorbent packed in an
adsorption cage 16 m2 in cross-sectional area and 16 cm in height. We
submerged three adsorption cages in the Pacific Ocean at a depth of 20 m
at 7 km offshore of Japan. The three adsorption cages consisted of stacks
of 52 000 sheets of the uranium-specific non-woven fabric with a total
mass of 350 kg. The total amount of uranium recovered by the nonwoven
fabric was 1 kg in terms of yellow cake during a total submersion time
of 240 days in the ocean."