Trying to connect to an Microsoft Sql database but get error

I am trying to establish a connection to a Microsoft Sql Server express edition databse called PrimeMinisters and get the following error.

Cannot open database "PrimeMinisters" requested by the login. The login failed. Login failed for user 'DESKTOP\Arian'. 

I am asuming I need a user name and password but as this is just for home use I dont see the need for a username and password in the connection string.

I added the database as a new connection in database explorer and I will upload the source code for the connection string I used

How can I overcome this error message and establish a connection with the database?

Kind regards