5 ms·

As a layman, I wonder about the connection between primes and random numbers. Obviously, the primes are not actually random, but they seem to exhibit a lot simi

As a layman, I wonder about the connection between primes and random numbers. Obviously, the primes are not actually random, but they seem to exhibit a lot similarity to random numbers in that they are chaotic over short intervals, but seem smoother and better behaved over long intervals.

deleted 9y ago
[deleted]
deleted 9y ago
[deleted]
deleted 9y ago
[deleted]
mixedmath 9y ago
I would say that this is one of the things that have inspired many mathematicians to study and try to understand the primes. Many results in classical analytic number theory measure things which deviate away from the assumption of randomness. And mathematicians are often very interested in recognizing new times when things are not as random as they appear (such as [1] recently, where it turns out that there are biases between congruence classes of consecutive primes, even though in the limit things are "random"). [1]: https://terrytao.wordpress.com/2016/03/14/biases-between-consecutive-primes/ https://terrytao.wordpress.com/2016/03/14/biases-between-con...
osivertsson 9y ago
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics [1] is a nice read if that kind of question occupies your mind. [1] https://en.m.wikipedia.org/wiki/Prime_Obsession https://en.m.wikipedia.org/wiki/Prime_Obsession
- fao_ 9y ago
  Non-mobile link: https://en.wikipedia.org/wiki/Prime_Obsession https://en.wikipedia.org/wiki/Prime_Obsession
- heinrichf 9y ago
  And Marcus du Sautoy's "The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics" [1] is an even nicer one. [1] https://en.wikipedia.org/wiki/The_Music_of_the_Primes https://en.wikipedia.org/wiki/The_Music_of_the_Primes
ThrustVectoring 9y ago
Is 4 a random number?