The documents show Amazon's total US audience for all video programming on Prime (which includes the shows it licenses from other companies) was 26 million customers. Unfortunately, we do not know the figures for its global audience.
The first season of The Man in the High Castle drew in eight million US viewers early in 2017. The show cost $72 million to make, and attracted 1.15 million new subscribers worldwide according to Amazon's calculations. This means that the show brought in Prime members at an average cost of $63 per subscriber.
It's unclear how Amazon works out a customer's motivation for joining Prime, but according to Reuters a "person familiar with [Amazon's] strategy" said the company "credits a specific show for luring someone to start or extend a Prime subscription if that program is the first one a customer streams after signing up".
That metric is called a 'first stream', and is used to calculate how expensive the viewer was to acquire by dividing the show’s costs by the number of first streams it had. The lower the figure, the more profitable the show was.
Ultimately, this is all for the express goal of getting more people into the Prime ecosystem so they can spend more money on physical products - the more people use Prime for their music streaming or video bingeing, the more they are likely to buy through the shopping site and use its express shipping.
Analysts estimate approximately 75 million customers worldwide have Prime subscriptions - which includes half of all households in America.