On Windows, R requires a compiler so you'll need to [follow the instructions](https://github.com/stan-dev/rstan/wiki/Installing-RStan-on-Windows) provided by `rstan`. The key step is installing [Rtools](http://cran.r-project.org/bin/windows/Rtools/) before attempting to install the package.
The major dependency that Prophet has is `pystan`. PyStan has its own [installation instructions](https://pystan.readthedocs.io/en/latest/installation.html). Install pystan with pip before using pip to install prophet.
On Windows, PyStan requires a compiler so you'll need to [follow the instructions](http://pystan.readthedocs.io/en/latest/windows.html). The easiest way to install Prophet in Windows is in Anaconda.
Make sure compilers (gcc, g++, build-essential) and Python development tools (python-dev, python3-dev) are installed. In Red Hat systems, install the packages gcc64 and gcc64-c++. If you are using a VM, be aware that you will need at least 4GB of memory to install prophet, and at least 2GB of memory to use prophet.