Hints, but no cheating by checking the pop reports... No it's not counterfeit Yes those are slab prongs (NGC if you don't recognize them they look huge because a trime is only 14mm) No it's not details graded (yeah, double headshake on that) Pop is 1 at this grade...
MS 60? Looks like high xf details (maybe low AU details). Also, it is worthy of posting here: https://www.cointalk.com/threads/rare-graded-coins.288917/
How is the luster in hand? The luster can make a big difference. I believe the piece is AU. Right now, I'm leaning towards AU50.
Your hint - and the fact that 1872 Business Strikes are scarcer than hen's teeth - lead me to guess it's an impaired Proof. We'll call it PR50.
I will say Proof 58 and will tell you this is an RPD -001 1872/2 see hook like barb on the mid of the two? Proofs were also struck from the same dies as M.S. coins. Only1000 1872 TCS business strikes were struck in 72.
Thanks for the pickup point. If they use the same dies how do you tell a business strike from a proof? The pictures on PCGS coin facts show a slightly different placement of the seven (in-line vs above the 82 tops).
I'll answer your question generally. The services would look at several factors including whether the rims are squared (consistent with a proof) or rounded (consistent with a business strike); the strike of the coin; and the reflectivity and whether there are patches of mint frost/luster in protected areas (like the recesses of a shield) that may be used to distinguish a prooflike business strike coin from a proof coin.
@SuperDave nailed it first. 1872 3CS PR50 NGC. NGC Census: (1/201). PCGS Population: (0/286). Mintage 950 It showed up in Heritage's Tuesday internet only auction - I think hurt by the proximity to the nice coins at FUN. If it had been a business strike it would probably have been XF details (at least judging by the photos - don't have it in hand yet). And a perfect fit into my XF 3CS set. And probably, i don't know, 2-5x the price. The whole submission is a little sad, basically looks like some of mine where I bought a bunch of stuff I liked and sent it off to NGC. Boom... -012 is an 1863 3CS Proof Details, improperly cleaned -016 is an 1859 3CS Uncirculated Details, improperly cleaned With a couple of cleaned and questionable color indian heads. And an improperly cleaned 1884 2c. The gem is -014 an MS65 1920 Pilgrim commem.