Since Bob has mentioned that two-part video, let me add that two important things got cut from it:
1. Right at the beginning of Part 1:
The quote at the start that this is one of the most remarkable facts in mathematics comes from Don Zagier's Inaugural Address in Bonn in 1975, in a talk called The First 50 Million Prime Numbers.
You can see it here:
2. Right at the end of Part 2:
For getting primes on a line, the earliest set of 20 primes that lie on a line has the prime 509 at the end of the line. See sequence A376187.
In contrast, the first time there is an arithmetic progression of 20 primes, the prime at the end of the line is 572945039351. See sequence A005115.