Calculating the "Cannabis Number"

A classic Gary Larson cartoon depicts the "Libraries of Hell". All the books are labeled "Word Problems". Most people in high school hated word problems. I liked them, was good at turning concepts into math which is probably one reason I was attracted to physics. Carrying out the computations was another matter; I was and still am inept in arithmetic. Let my computer do the computations, I say: doing arithmetic is demeaning to humans. Solving word problems, on the other hand, is a worthwhile pastime.

A few days ago, while soaking in my outdoor tub (like Archimedes who is rumored to have made fundamental physics discoveries in his bath) I was pondering the 4:20 phenomenon in which first the time 4:20 PM and later the date 4/20 became associated with the smoking of marijuana. I was concerned that this number seemed arbitrary and wondered if it might only be an approximation to a more precisely defined "cannabis number" -- a number that is more than a mere human convention but is instead a perfect mathematical concept that dwells not only on Earth but in the eternal world of Platonic Forms. The Cannabis Number CN -- a number that can be calculated mathematically.

So here is my proposal: the exact "cannabis number" is not 4:20 but that time shortly after 4:20 when the Big Hand exactly overtakes the Little Hand. More precisely CN is the number of minutes past 4:20 at which this coincidence occurs.

One might even imagine that 4:20 is the approximate time to start smoking but the veils between worlds actually open at the somewhat later time expressed by the cannabis number.

CANNABIS NUMBER
When the Big Hand overtakes the Little Hand
When the Little Hand lies underneath
When the Big Hand covers up the Little Hand
When the Little Hand's on the bottom
And the Big Hand's on top
That's when the doors must open
That's when we must smoke pot.

That's how Nick defines CN. But what is the numerical value of this "cannabis number"? I leave this calculation as a problem for my readers. Please post your answer in the comments section. Hint: the problem is not as hard as the problem faced by the Russian at the blackboard.