Tests more conclusive after certain period only.
1 Antigen would appear in the presence of an HIV infection as early as 1st week of the infection itself. In some individuals due to its low titre, test may take time to pick up these antigens. So after 4 weeks there would not be false negative results with this test.
HIV 2 can be identified only with the antibody test as far as the tests available in market. The antibodies
also may be recognized as early as 6-8 weeks, in some individuals antibody production could get delayed up to 12 weeks. So the test becomes more conclusive after 12 weeks. That is the idea.
Anyhow your risk is very low.