While earlier reports of the Samsung Galaxy S 4 I9500 (Exynos) being rooted were fake, a real root method has been found for the I9505 Qualcomm model. If you’re wondering who managed this, it was none other than Chainfire, a very famous developer for good reason. Despite the standard method of injecting su into a stock ROM and flashing with Odin not working (due to security Samsung put in specifically for KNOX, to keep it safe for business use), he figured out a method using is own app, CF-Auto-Root.
And to please everyone, he posted all the instructions. So if you happen to own a Qualcomm-powered Galaxy S 4 and want to go through the risky procedure of rooting it, hit the source link for instructions.