Since the early times of SharePoint we receive support cases where a customer receives the following error message when using custom code with SharePoint:

"The Web application at http://server:port/ could not be found. Verify that you have typed the URL correctly. If the URL should be serving existing content, the system administrator may need to add a new request URL mapping to the intended application"

Here are the most common reasons this error can occur:

1. The code is executed on a different machine - The SharePoint object model (except the Client API) requires to be run on the SharePoint server itself. It is not possible to run the application on a server which is not within the same SharePoint farm the code is trying to access.
2. Insufficient Rights on the site collection - The code is executed in context of an account which does not have read permission on the site collection
3. Incorrect Url being used - Verify that the site works correct in a browser and double check that the server is correct registered in the AAM settings
4. Incorrect bitness - The SharePoint object model needs to be executed with the same bitness as the operating system. That means you cannot use the SharePoint object model in a 32-bit application if the Operating System and SharePoint are installed as 64-bit version. Ensure to compile the project using the correct bitness (64-bit on a 64-bit machine vs. 32-bit on a 32-bit machine)
5. Incorrect .NET framework version -  Ensure that the project is configured to use .NET 3.5. .NET 4.0 cannot be used with the current versions of SharePoint