I think the definition of ‘experiment’ gets tricky and confusing when you are talking about math specifically. When you talk about finding the distribution of prime numbers and using that to arrive at a more accurate model for your prior probability of 3339799 being prime, that is an experiment.
Math is unique in that regard though. For questions about the real world we must seek evidence that is outside of our heads.
I think the definition of ‘experiment’ gets tricky and confusing when you are talking about math specifically. When you talk about finding the distribution of prime numbers and using that to arrive at a more accurate model for your prior probability of 3339799 being prime, that is an experiment.
Math is unique in that regard though. For questions about the real world we must seek evidence that is outside of our heads.