Not the same page, but one just as good; I'm not sure what happened to that reference, it was cut and paste from my browser address bar. The definition on the wikipedia page you found contained a strange use of "any": "any" meaning "some". This is sort of logical but is a very unusual usage, so people get confused when "any" is used like that, and sometimes think it means "every". That wikipedia page has now been corrected and uses "some" instead of "any" which should be clearer.

The writer of the original definition on the wikipedia page can be excused because he probably though that misinterpretation of that "any" would be avoided by that little word "conversely", which is saying that "prime" is the converse of "non-prime" which is defined immediately above (and the converse of "it isn't in any candidate key" is "it is in some candidate key") but it's better to avoid unusual usage and aim for clarity in something like wikipedia.