aviwl

What factors do you think contribute to the ability of the US to attract the best?

By "Jay Scaler" do you mean Jay Chaudhry?

As stated in the article, those conjectures were made in 1923. The recent quanta article https://www.quantamagazine.org/20160313-mathematicians-disco... involves a new correlation discovered in the primes, which means that the statistical model is more interesting than we previously thought.

For a mathematician's perspective on the recent breakthrough, I recommend https://terrytao.wordpress.com/2016/03/14/biases-between-con....

There is no reasonable formula for generating prime numbers. So let's treat primes as if they were empirical data points instead of deterministic mathematical constants. From this lens, the statistical properties of primes are very simple to predict. That's what all these conjectures are about: finding out what sort of probability distribution would produce random numbers that look like the primes.

The author is making the following reasoning: Conjecture 1 and Conjecture 2 can not both be true. Conjecture 1 is believed to be true. Therefore Conjecture 2 is false, which implies that there must exist a heavy cluster of primes out there.