This question is somewhat more vague than you may realize.
One could call any rifle pressed into service for the purpose of hunting a 'hunting rifle'.
In so far as rifles made specifically for the task of hunting, ignoring questions of power and going purely with bore size the largest would be the 2-Bore rifle produced by individual gunsmiths for (largely wealthy) clients who want to have something unique. A 2-bore rifle has a bore-diameter of over an inch and fires more than half a pound of lead with a single pull of the trigger.
While one is hard-pressed to find a bigger-caliber hunting rifle, there are a few contenders in this heavy weight category such as the .700 AHR and .600 Overkill made by American Hunting Rifle, the .700 and .600 Nitro Express family from Holland & Holland of London, and and a myriad of other calibers from various producers such as .729 Jongman's, .585 Nyati, .500 Jeffery and others. Meanwhile there are many old muzzle-loading firearms in the .75 caliber range, to say nothing of the earlier Bore-Rifles. None of these however have more raw size than the 2-Bore.
In so far as what would be the 'most powerful' hunting rifle, that would be a different discussion entirely. I mention this because many people make the false-equivalence assumption that bore-size and power are one in the same when they are not.
Benjamin (Owned by Crosman) has a new Benjamin Rogue it is a .357 caliber. At present it will be the largest Pellet rifle made with the Benjamin name. Yes it is a hunting rifle. The next largest Benjamin rifle is the Benjamin Marauder .25 caliber. Sam Yang make a 50 caliber and a 44 caliber hunting air rifle.
Depends on what you are hunting. See the link below to the Illinois Game Regulations.
it depends on what your hunting
H&R Handi-Rifle
A "sniper rifle" is simply a rifle employed for that purpose. So long as the "sniper rifle" meets the criteria and restrictions for hunting firearms in the state you're hunting in, you can use it.
Hunting rifle scopes come in a wide variety and are easy to find online. Some websites like The Scope Smith and Optics Best Buy offer hunting rifle scopes.
You could use any magnification you wanted- but extremely high powered scopes would be useless- the field of view would be so small, you could not find your target. The largest I use on a varmint rifle is 24X- and I would not use that on a hunting rifle. Military sniper rifles generally use less powerful scopes than that.
yes
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One of the main advantages of air rifle hunting is that it's easy to use, gives you cheap practice and is also good for hunting small game. One of the main disadvantages or air rifle hunting is the fluctuation of pressure in relation to ambient air temperature.
It all depends on what you are hunting.
The .950 JD Jones is the largest sporting rifle caliber made.