Number one

Which of the above is correct or either one is fine?

Are. "Number" is plural.

Um, well, "number" is singular, but "are" is correct.

At first I also thought it was singular but figured you wordsmiths know better.

If you turn the sentence around it is:
A number of problems are/is there.
If "number" is singular it would take a singular verb--"is"-- since problems is the object of a prepositional phrase.

Knocking out the prepositional phrase and the sentence reads: "A number is there" or "There is a number" which sounds perfectly ok.

But using the singular sounds awkward: "There is a number of problems".
Help!!

From the Chicago Manual of Style:

Number as a collective noun takes a singular or plural verb depending on the article (definite the or indefinite a) that precedes it:

The number of pizzas ordered this year has doubled.

but

A number of studies have shown that stuffing a pizza with spinach triples the edibility of that sinewy vegetable.

I did not know that.
Thanks for the info.

Yeah, great, I like it too. But that sentence! Did it come from the Chicago Manual of Style? It is correct, but a poor example. We see s sentence about stuffing a pizza, and suddenly it becomes a sentence about a vegetable, interrupting the flow. Better to let us know right away that this is a sentence about spinach. Still not good, but possible: "...using spinach as pizza stuffing triples (triples?) the edibility of that sinewy (muscular?) vegetable." SS

The usage is idiomatic.
THE number of cats/dogs/etc on the street IS increasing.
A number of cats/dogs/etc ARE roaming the street.