Probability on Understanding the Riemann Hypothesis
https://riemannhypothesis.info/tags/probability/
Recent content in Probability on Understanding the Riemann HypothesisHugo -- gohugo.iomarkus@recommend.games (Markus Shepherd)markus@recommend.games (Markus Shepherd)Wed, 31 May 2017 05:41:25 +0000The Prime Bet
https://riemannhypothesis.info/2017/05/the-prime-bet/
Wed, 31 May 2017 05:41:25 +0000markus@recommend.games (Markus Shepherd)https://riemannhypothesis.info/2017/05/the-prime-bet/Let’s say you sit in a pub, minding your own business, when all of a sudden a stranger walks up to you and offers you a bet:
We’ll choose two positive integers at random. If they have any divisor in common (other than \(1\)) I’ll pay you a dollar, else you’ll pay me a dollar. Are you in?
Apart from the question what kind of establishments you frequent, you should be wondering: is this a good bet for you?Are Primes Independent?
https://riemannhypothesis.info/2013/11/are-primes-independent/
Sun, 24 Nov 2013 14:32:23 +0000markus@recommend.games (Markus Shepherd)https://riemannhypothesis.info/2013/11/are-primes-independent/The question may sound silly, but I hope it will become apparent that it’s very reasonable to ask. What we will examine here is the probabilistic interpretation of the prime distribution. So, essentially we ask: “What’s the probability that a randomly chosen number is prime?” Those familiar with some basic probability theory know the notion of independency in this context, so the question I’m basically interested in here is if the probability to find a prime is independent of the preceding or following numbers.