EDM makes a 408CheyTac, (Cheyenne Tactical), that shoots a 419gr solid copper bullet at over 3000fps. The bullet stays ultrasonic past 2200 yards. I have shot one of these out to a mile and it does an incredible job of it too. It's hard to find the right condition to pull it off but on a day with little or no mirage it's capable of some very long shots.
Another one to look into is a 338Edge. Defensive Edge, (Shaun Carlock) out of northern Idaho built mine. Check out his website and look at the canyon rifle. Not a bad price compared to the 408 at $10,000.
Kirby Allen makes a 338AllenMag which is a 408CheyTac necked down to 338 caliber. It's a screamer!
There's other guns that are capable of ranges that your after but these are the only ones I'm familiar with.
Here's a question for you, are YOU capable of shooting that far? Do you know how to take spindrift, elevation, humidity, bullet BC, velocity, full/half/quarter-value wind and other facters and make a shot count? Are you a good enough shot period? Shooting that far is a whole new world to the average shooter.
"My sickle has a boattail"
"hidden soles leave .308 holes"