If I remember correctly, I purchased a bunch of this stuff years ago and it was marked as being 8mm Mauser... but the closest thing to 8 on the headstamp is 79

How can I be certain this is ammo safe to run through my old mauser 8mm?

8mm Mauser is actually 7.92x57.  

Link

ETA:  Measure the bullet diameter too.  If it was made in '57, it should be .323".  How old is the rifle?

Thanks for the link

The rifle in question is stamped 1944... she's no beauty queen, but complete and seems to be in good enough condition for a test-fire session.

I'm not sure exactly what it is, but no 8mm Mauser ammo has the NATO cross. I bet it is Port 7.62x51 like posted above.
That's a Turkish Mauser. GTG with full power loads.

What do the numbers correlate to, out of sheer curiosity?

Crap... shooting session postponed until further notice

No offense intended, but if you are not completely familiar with any ammo ( ie.. funky headstamps, etc. )  don't use it until you know what it is.I strongly suggest you get some factory 8mm Mauser that is marked as such. That way you have something to compare too.
Again no offense, but the round shown is a .308 Winc. or 7.62x51, and not really that close looking to the 8mm...( I know we all have to learn somehow... ).... and again I'm not trying to be a jerk, I'm saying this because No One here would want you to get hurt. Firing a .308 in your chamber would have been very bad.

This photo shows the size differences....

From left to right....9.3x62mm,  .30-06,  7.92x57mm ( 8mm Mauser),  6.5x55mm ( Swedish Mauser ) , .308 Winc.

I'm just concerned that you aren't sure what your ammo looks like and that you maybe aren't that familiar with shooting. I know this sounds condescending, but it is not meant to be.

I completely agree... which is why I posted the question here first!

I really have no need to shoot this old rifle, just attempting to ID the ammo I have.

I have (2) old 8mm Mausers in my collection, among a dozen or so 308/7.62x51 chambered rifles.

Should I disassemble this lot of ammo in question?

I will attempt to get some accurate measurements to the best of my ability and post them up

No , that .308 ammo is good stuff. Shoots great in my M21. It is indeed Portuguese.

Thanks for being patient with my comments.

The above photo should help visually.

Well, I feel like an ass...

Long story short I am digging through a bunch of various ammo that I have had stuffed away for 10-15 years... I do not have any "factory" 8mm Mauser ammo on hand to compair to, but when I ran across this lot loaded on 5rnd stripper clips my first thought was that it was for the Mauser's... glad I asked first!

And thank you all for you valuable input! I love this site

LOL , we've all done something like this...

OK, so what are the numbers on that ammo indicative of if they don't relate to caliber or year of manufacture?

I believe it was made by BF = Fábrica Nacional de Munições de Armas Legeiras, Chelas, Portugal , 79 = 1979  , 57 = Lot 57

I have a bunch of Port with the same headstamp and it looks the same.

Thanks