  We first show a counter intuitive result that in the ring of real valued
continuous functions on $[0,1]$ non maximal prime ideals exist. This is a
standard proof and a well known result. Interestingly, a non maximal prime
ideal in this ring is actually contained inside a unique maximal ideal. We
arrive at this result merely by looking at the zero set of ideals in this ring
and by making simple geometrical observations. We end by leaving the reader
with an interesting open problem that logically follows from this article.
