What was your risk, please?
Yes, a 4th generation HIV test can be considered conclusive at 4 weeks in your case, at that time this test is said to be about 95% accurate. For a low risk exposure, the above number is sufficient to rule out HIV infection.
This test is best at 28 days, since the average time to sero-conversion is about 21 days, a week post that (28 days) most infected individuals would start to produce detectable amount of antibodies. However- although very unlikely, if the antibodies are not produced at that time, P24 antigen would be detected since the body would be in process of sero-conversion.
If you wish to be conservative and want an absolute confirmation, a test at 6 weeks will rule out HIV infection with an accuracy of 99.9% since any possibility of slight delay in sero-conversion will also be ruled out with this one. This is mostly to cover for the theoretical risk.