How to estimate numbers of a production run

I hope I am asking this in the right thread and more importantly it makes sense.

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

The item that these numbers have been assigned to have all now been produced and sold, but the total amount in circulation is not known. it is estimated the number could be 1,000 to 5,000 based on past and similar production runs.

My question is, can a statistical process be applied to find an estimate of how many items were produced from these 163 known serial numbers within the known range?

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.