1
$\begingroup$

Are there some simple, unifying and convincing models about the properties we expect for the prime-numbers :

  • that would be much stronger than the usual probabilistic model $\mathcal{P}(n {\scriptstyle\text{ is prime}}) \approx \frac{1}{\ln n}$,

  • and that would answer at least asymptotically to most of the conjectures about prime numbers ? (in particular : generalized Riemann hypothesis, Goldbach conjecture, density of twin/factorial/Mersenne primes, least prime in subsets of the integers ...)

Or is it really in the nature of prime numbers, that the number of very difficult problems about them will be high forever ?

  • 1
    And can you criticize the question please ? I have the intuition there is an important concept behind, but I cannot get it. – 2017-02-07
  • 0
    There is only one model. It is based on convergence of odd and even numbers. – 2017-02-08
  • 0
    @usir0 what do you mean ? – 2017-02-08
  • 0
    I am thinking about to put a question and explain by the way my discovery on how numbers get into composition. At the moment I am still testing my hypothesis, since it uses different algebra. – 2017-02-08
  • 0
    @usir0 I'm not asking for *a wonderful new research of some young genious*. Do you understand the conjectures I mentioned, and how they are related together ? – 2017-02-08
  • 0
    Yes, I do. I don't agree with most of them. – 2017-02-08
  • 0
    @usir0 how would you explain in the same time (with the same model for primes) the twin prime conjecture and the riemann hypothesis ? – 2017-02-08
  • 0
    Twin prime conjecture is easy to see since general model for primes is a superpolynomial which comes in two forms with arithmetic progression inside. With all respect to Riemann, he could not see it on the Cartesian coordinate plane, because he assumed that negative times negative is positive, which I can disprove by revealing extended method of Fermat's factorisation based on zero-balance symmetry plane. – 2017-02-08
  • 0
    I hope don't distub with this new contribution, since I don't know if it is (or how it is) related to your question. Then just to add that there is an article that can be interesting. It is Michael Rubinstein, *A Simple Heuristic Proof of Hardy and Littlewood's Conjecture B*, The American Mathematical Monthly Vol. 100, No. 5 (1993). Good week. – 2017-07-18
  • 1
    @user243301 I don't have access to it. Of course there are some convincing models (= heuristic argument) for the twin prime conjecture or the RH alone, but those don't include Goldbach nor the generalized RH. – 2017-07-18

0 Answers 0