The answer to the question is an ancient philosophical question: Ship of Theseus. As Organic Marble mentioned in his comment which could have been an answer:
The SRBs were made up of segments, and the reuse was at the segment level.
The obvious lower bound for number of SRB segments produced would be eight: four SRB segments per side per launch. We can double that to 16 as this photo shows two STS stacks on the pad together.
Each SRB segment was rated for 20 launches. This document for the SLS Qualification Motor shows booster segment serial numbers in use on that test:
O32, O89, O43now, L82, L89n, L109, L98n, L92, L95n, O59
I'm sure that I've misread or misinterpreted that slightly, but for purposes of estimating population the numbers will do.
If we apply the German tank problem to that data, then we can estimate 120-130 total segments that were given serial numbers, as the higher serial numbers are better represented. Divide 120 by 4 segments per SRB, and I would say that enough SRB segments were produced to build about 30 SRBs, given enough nose caps, nozzles, and other components.