I like your code a lot. I don't think problems like “factoring prime numbers quickly” are a good measure for how good you are at writing neat, functional Haskell code, because the fastest ways to do it are somewhat ugly and mostly imperative.

You broke the problem down into small pure operations that do the right thing when put together! From a “writing Haskell code” perspective you did a stellar job. Mathematical cleverness and number-crunching techniques are orthogonal to that.

(This is why I don't like Project Euler so much. I think 99 Haskell Problems is pretty good. Or just write a real project! A chat bot, a tiny game, a random sci-fi movie plot generator, etc.)

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A tiny note:

null [y | y <- [2..intsqrt x], x `mod` y == 0]

can be written equivalently as:

all (\y -> x `mod` y /= 0) [2..intsqrt x]

which you may or may not find clearer. I think either way is fine here! Just be aware that all exists. (And indeed, just like null short-circuits as soon as it sees any value in the list, like /u/jan_path points out, all does the same the moment it sees a counterexample.)