Don't go there, no reputable journal can validate your work in a four week time frame.     

If they do promise that, for a fee, you can bet this is a predatory journal. (Meaning: their business model is to publish as much as they can for substantial author charges, rather than to validate and reject submissions for scientific reasons.)

Now if you are concerned with priority, just posting the manuscript on arXiv will establish that. So there is no real need to chase a rapid publication time in this day and age.