Not sure, the serial doesn’t follow the usual three digit or A+ three digit Paramount sequence. If I had to guess I would say 38-40 is possible, the ball end seat stays are typical on early bikes.
This bike was rode hard and put up wet, it’s been crashed and repaired. I bought it for parts for my 39 Paramount, it came with a complete crankset, headset and hubs. I’m in the process of collecting parts to make it a complete bike again.
All the serials on these early Paramounts have stampings that don't look so nice, and they are all, at least the ones I've seen, read from the rear of the bike. Here' a typical stamping, and this is also typical on the prewar and wartime New Worlds and Superiors with the three piece cranks.
I have emailed Scott Wastyn in the past about another bicycle, he replied that the serials on their bicycles were at the customer’s request and could be anything they wanted. This was great for recording a single bike to an owner, not so great for reference. This bike has moved around, it was picked up by Hilary Stone in the Midwest and sent across the Atlantic, purchased by yours truly and brought back stateside. I’m reasonably sure it’s a Wastyn built Paramount, and at the very least Wastyn built.
I think @GTs58 was on to something, maybe restamped at the time of repair. The serial is upside down compared to other Paramounts and in a different location. I don’t know if the”X” is covering part of the old number or has some other designation-meaning.