The first operational medium range model is the GFS or Global Forecast System model.
This one came from the old AVN (Aviation) computer model. This one forecasts out to 2 weeks, but with a catch.
The first week has more than double the resolution of the second week. That simply means the first week is useful, but the second week is better just recognizing trends.
That doesn't mean it can't get something accurately two weeks out, but it does mean you shouldn't gamble on that two week forecast.
Also, with the GFS, the atmosphere is treated as waves mathematically rather than grid points. It is called a spectral model. Just FYI, not really important here. I generally use this one for comparison to other medium range models beyond 3 days.