I found that after uninstalling a product with this product identifier
iTunes Connect does not allow this identifier to be used again. However, I found a workaround. Product identifiers are case-sensitive, so if you simply change your capitalization when re-using the product identifier, iTunes Connect will not stop you. (However, according to Il Malvagio Dottor Prosciutto, this can be risky.)
In addition, during short-term testing, it does not appear that your product identifiers must be unique throughout the store. I tried some fairly common words that I thought others could use for the product identifier, and they all worked.
Please note that the products I tested on had different recurring subscription dates in the app store. I do not know if the rules are different for other types of products.
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