I think you should have written it "resistance" in stead of "support". As it is trying to knock and cross 4000, then it should be attributed as a "resistance".
Now if the sense of the question is in the context of 4000 as the hurdle then I agree that yes it is. And it is trying to consolidate and the next leg from here is up only. If it will be able to break above 4000 level then the next resistance will be 4400 followed by 5200 and 5500 respectively. In my view, 5500 is a major and very very tough resistance and in reality it is the multi year resistance. So it will be interesting to see the price action of BTC when it reaches that zone. But as the altcoin market is firmly up and steady now, BTC turn will also come and it will also rally but may take some time. The altcoin rally is one of the clue that BTC next leg will be up.
The technical indicators of BTC chart are also hinting that there will not be any major downmove as RSI is stabilized, bollinger band is looking flat and other indicators are also showing signs of consolidation. So let's wait and watch what market offers from here on.
Note- This is not a financial advice.