K&E (Keuffel & Esser) is one of Longines' contractors that made cases in the US to Longines' specs for Swiss dials/movements to be installed. It's certainly solid 14K gold. I have the diamond indice version of that watch (reference 2770). It's a caliber 370 made in the 60's. Looks like a good buy to me.
It is approximately 33 mm in width without the crown.
ps - We call that bezel pattern florentine.
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