Giacomo wrote: So to some extent the primes are tamed, because we can make statistical predictions about them, just as we can about coin tosses.
jshort wrote:Wouldn't this mean that the primes are untamed because of this. After all, the tossing of a coin is random..
jshort wrote:With regards to "true randomness", even though the primes may not have this property, they are still chaotic enough that I believe one can make conclusions about them by conclusions made about coin flipping (we just won't be able to prove these conclusions).
Giacomo wrote:The primes are not random. If you ask for the first 100 primes, you always get the same answer, but if you ask for the first 100 coin flips, you get different answers every time.
Giacomo wrote:Also, the error term for primes represents a difference between two deterministic functions; it's vague because we don't know a lot about one of the functions, not because it's random.
Giacomo wrote:There are a number of intriguing but unexplained analogies between the behavior of the Riemann Zeta Function and some probabilistic problems, although no one seems optimistic that these can be used to prove RH.
smokeybob wrote:I found that very helpful. And thank you!
So do these L-class functions have a particular maximum order? Or are they just way harder "polynomials", where the order goes up to infinity. But we find some interesting properties about, zeroth, first and second order polynomials and real-life things - is this similar to L-class functions, but on steroids?
Let u(n) be the mobius function and let M(x)=sum(n less than x) u(n). It can be shown that the claim that M(x)=O(x^(1/2 +e)) for every e greater than 0 is equivalent to the Riemann Hypothesis.
Now it can be shown that if K(x) represents the sum of heads minus the sum of tails obtained from a coin that is flipped x number of times, then we also have K(x)=O(O(x^(1/2 +e)) for every e greater than 0. Unfortunately, the proof for this case requires us assuming that the coin flips are random. This raises the following interesting questions.
1. Is there a fundamental difference between the Riemann Hypothesis, and the cion flipping problem?
2. Do we have to prove some sort of randomness condition for the primes numbers in order to prove the Riemann Hypothesis?
3. Is such a proof even possible?
gnom15 » February 24th, 2019, 12:36 pm wrote: arXiv:0810.0095 "Modeling the creative process of the mind by prime numbers and a simple proof of the Riemann Hypothesis"
gnom15 » February 24th, 2019, 12:36 pm wrote:The key is prove that prime numbers are inherently or by definition unpredictable.
gnom15 » March 4th, 2019, 1:37 pm wrote:sounds like you know quite a bit about crank
gnom15 » March 4th, 2019, 1:53 pm wrote:Primes may be produced by a deterministic process but that does not mean primes can be predicted.
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