In short, if I say, “There is a number of reasons written on the paper,” expect to see a figure such as 5, 12, or 67. If I say, “There are a number of reasons written on the paper,” expect to see the reasons themselves. And if I say, “There’s a number of reasons written on the paper,” well, it really depends on just how casual I’m being with my speech — but don’t expect me to use it in earnest in formal written English. There are a number of reasons I wouldn’t.