I have been looking at different barrels on line today.
A #4 sporter is .650" at muzzle - .423 and/2=.113" wall thickness at muzzle
A#5 sporter is .700" at muzzle -.423 and/2=.138.5"

Is the lighter barrel with .113" sufficient, or do I need to go for the .138.5" wall thickness.
The front sight and the banded sling swivel base will be soldered on. The rear sit may be screwed on, but the barrel will be thicker there.
Thanks.

I always read rule of thumb was .125" minimum thickness at the business end. I have a 9.3x57 that's thinner than that. I think you can get .125" from the #4 barrel, just shorten it down some or have a custom profile turned - that would be your best bet. Also, not all #4 barrels are exactly the same from different manufacturers. Look around.

.100" is the minimum and people have gotten away with .080" on Nitro Express barrels for years.

Thank you for your great input. That takes a great load off of my mind.

I didn't know you were worried about strength; I thought it was about total weight.
Do not worry about barrel wall thickness at the muzzle; there is practically no pressure there and it can be paper thin. Ok, maybe not paper, Look at double rifles. Just checked a 450 Nitro; muzzles are .083.
Balance is the reason barrels are thin at the muzzle and there is no rule.
You can't rely on the banded front sight for strength though.

Zastava factory barrels for the 458 Win Mag are .660 at the muzzle which leaves a .101" wall thickness

Thank you all. I'm a slow learner, but I write down what I learn.