Stat Analysis of categorical data: "You hypothesize that in the 17th century nobody lived for 70 years or longer in your country."

[BigBeachBanana]

I have just tried anticipated incidence 99.9% for the group 1 and 0% for the group 2 on this online calculator and got that the sample size is only 2 per group. Intuitively, it's wrong.

Click on View Calculation, it'll show you the equation. It should be a 2-sample t-test.

With such extreme differences, you can achieve statistical significance with a very small sample size because the two proportions are so different that even a small sample size will likely be sufficient to detect this significant difference.