Estimating a production number

I hope this makes sense.

I have a series of 163 serial numbers that fall between 77.681.001 to 78.786.366.

The items have now all been produced and sold, but the total amount in circulation (x) is not known. I only know of 163 and it is estimated the number could be 1,000 to 5,000 based on past and similar production runs.

My question is what statistical process can be applied to find an estimate of x, that is, can I get an estimate of just how many items could have been produced by only knowing these 163 known serial numbers?

I have heard of the German Tank problem is that something I could look at?

Appreciate some idea if an estimation can be ascertained through statistical methodology.

Thank you.