Do you mean rarest as in least abundant or rarest in appearance compared to other minerals?...i don't know either way.
i think there are minerals that are so rare we have not named them yet. gold diamond and platinum are not that rare compared to some. they are commercialy available and are sold openly to the public. there are minerals that are very rare. and i might not be 100% correct but i think there are minerals that decay so fast that we cant hold them in true state for long. painite is considered very rare, maybe even the rarest. peace.
Californium is rather expensive, from what I have heard. As are most of the synthetic elements, I guess.
Blue John is only found in one hillside in Derbyshire... Although it is a (unique) vareity of a fairly common mineral. The kryptonite metakron mentioned is officially known as jadarite (http://en.wikipedia.org/wiki/Jadarite)
As a geologist I would caution that any term needs defining. 'Mineral' has all types of definitions. Often it includes 'naturally occuring' in the definition but even that can be open to debate as man is a subset of Nature and anything we do is 'natural'. Other definitions include things like 'geologic' in origin, etc. Items that occur naturally through geologic process on Earth are difficult to measure. Few elements such as gold or diamond crystals are 'rare' as much as they are difficult to obtain. Man hasn't mined a trillionth of the diamonds available on Earth or a fraction of the gold but we've mined the easily obtainable deposits that are within our technological capability. Another way to put the question is what element or mineral makes up the least percent of the Earth's mass. I don't know and don't think it could be known. The elements such as technetium (spelling?) and promethium at atomic breaks (40 something and 60 something) are unstable so minerals, if any associated with these would be rare. There's just not enough info on the minutia of the makeup of the Earth below the crust. The answer: 'We don't know"
What's interesting is that we can often predict with good certainty that certain crystal structures should exist naturally without ever actually discovering them.
The rarest mineral is indeed thee female willing to couple. Disclaimer: This is meant as a joke and to bring joy to the other members of the community, please do not be angry :C~