Why is Rick and Morty's dimension called "C-137"?

The only significance I could find is that C-137 is Caesium-137, a radioactive isotope that is also the most dangerous byproduct of a plutonium explosion.

This could be a coincidence, and the actual abbreviation for Caesium is Cs, and it has not been confirmed by official sources, and is merely a potential point of significance.

As for in-universe, canonical or officially confirmed significance, there is no mention of it in the show or otherwise, so until there is, it can only be pure fan speculation.

There has been no reason given for the name. Given the naming format, it stands to reason that all dimensions are labeled used a default naming scheme, rather than each dimension having a personalized name.

C-137 just happens to be "our" Rick's dimension. There is no significance to the number, it's just what it is.

Or, better answered in the words of Rick:

Don't think about it.

I have also seen the Cesium - 137 theory at a lot of places. But personally, I feel that the reference is simpler. 'c' is the speed of light and 137 as in the fine structure constant which equals '1/137'.

There doesn't appear to be any canonical answer to the question other than the fact that they are from

a universe designated 137, which falls along the Central Finite Curve (CFC), hence (possibly) C-137

I'm bordering dipping in to fan fiction/speculation here, but it seems implied that the CFC is a collection of universes which are in some way more stable/accessible/useful/similar. Anything said beyond that WOULD be fan fiction (such as implying that the first Ricks to travel interdimensionally just counted up as they went, starting with their own as C-1)

OK, there seems to be no official or a "Canon" explanation for any hidden meaning to the name "C-137"

However, regarding Caesium 137 (to quote from it's Wikipedia entry),

"It is among the most problematic of the short-to-medium-lifetime fission products because it easily moves..."

To me that seems appropriate to the in-show character of Rick. He's dangerous, reactive and mobile.

Also, if you take Yatharth's explanation regarding the fine structure constant, then you could take that as uniquely PHYSICALLY identifying the universe from which Rick C-137 originates (given how many fundamental physical constants, including "c", are related to it).

...seems to be making the point that Rick C137 is "Our Rick"...

OK, this is pure fan speculation but I think Dan Harmon's subconscious mind might have been working over time when he chose that name.

It's very simple. It comes from the registry number on the side of the alliance search and rescue craft on the planet named Miranda in Serenity... the 2005 film that was based on the cult TV show Firefly. The creator of Rick and Morty is a big fan.

Don't believe me? Watch the movie, pause it when Mal and crew find the crashed search and rescue ship on Miranda... clearly visible on side of ship is C 137 in futuristic script.

It's basically the possibilities in the multiverse.

So C-137 would mean possibility 137 of the C Possibility, so it's a possibility inside a possibility, A-137 would have different origins of Rick and the possibilities of it, whereas C-136 would be very close to C-137.

For example, in the Citadel episode, the news reporters are from D-716. Even inside that there are many possibilities, so there are D-716, D-716 B, and D-716 C, and all three have different experiences as marked by their faces, but still such a close origin that they are all news reporters.

So according to this, when Rick and Morty ruined their dimension and came to this one, they were from a very nearby possibility, as they didn't skip a beat.

My opinion is that's is the amount of dark energy in that universe. For example in our universe the amount is 0.000000000000000138 that is very close to 137 the Rick's universe. In the strings theory there are multiple universe, every universe has a different value and so different results based on this number. Take a look at this video: