This is true. Although, I’m not sure how many medium size companies have their own Prime Ministers.

Your first few weeks at any company in any role, though, are well spent meeting people and learning the product really well.

I also like to get or sit in on a sales demo and an onboarding call.

Since I've seen a growing number of Chief Of Staffs in startups, I'd guess the number of companies with Prime Minister roles is non-zero.

Maybe even with very sensible titles like 'Junior Prime Minister'.