[seqfan] Re: Distribution of the Prime Numbers in a Polynomial

[israel at math.ubc.ca]

Nonsense. For example, there are no primes in the sequence n^2 + 2 n + 1. 
Bunyakovsky's conjecture states that a polynomial f(n) has infinitely many 
primes if 1) it is irreducible, 2) its leading coefficient is positive, and 
3) f(n) have no common prime factor. But this is still very much open. In 
fact, we don't even know a single nonlinear polynomial that provably 
contains infinitely many primes.

Cheers,
Robert Israel

On May 16 2017, Charles Kusniec wrote:

>Dear SeqFan Members,
>
> 1- At https://en.wikipedia.org/wiki/Prime_number_theorem "In number 
> theory<https://en.wikipedia.org/wiki/Number_theory>, the prime number 
> theorem (PNT) describes the 
> asymptotic<https://en.wikipedia.org/wiki/Asymptotic_analysis> 
> distribution of the prime 
> numbers<https://en.wikipedia.org/wiki/Prime_number> among the positive 
> integers."; 2- Positive integers is a linear recurring sequence and the 
> set of it's elements form a group; Now, considering a parabola 
> x=ay^2+by+C where a, b, and C are integers and a>0, (so, if there are 
> negative elements they will be finite) 3- All sequences of the form 
> x=ay^2+by+C are also linear recurring sequences and also form a group; 4- 
> There is an isomorphism between each group aL^2+bL+C and integers group 
> where coefficients (a;b;C) are integers ; 5- So, distribution of the 
> prime numbers<https://en.wikipedia.org/wiki/Prime_number> among the 
> positive integers or any sequence of integers of the form aL^2+bL+C are 
> both asymptotic. 6- If it is true for a Parabola, will be true for any 
> Polynomial.
>
>Best regards,
>
>Charles Kusniec
>cel.: +55 11 987474974
><mailto:ck at centertap.com.br>ck at centertap.com.br<mailto:ck at centertap.com.br>
>
> Esta mensagem e/ou anexos contém informações confidenciais para o 
> destinatário, tem fins específicos e é protegida por lei. Se você não é o 
> destinatário desta mensagem, você deve apagá-la. Qualquer divulgação, 
> cópia ou distribuição desta mensagem, ou qualquer ação tomada com base em 
> tal, é estritamente proibida.
>
> This message and/or attachments contains confidential information 
> intended for a specific individual and purpose, and is protected by law. 
> If you are not the intended recipient, you should delete this message. 
> Any disclosure, copying, or distribution of this message, or the taking 
> of any action based on it, is strictly prohibited.
>
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>