# [seqfan] Re: A problem with de Polignac numbers

Tomasz Ordowski tomaszordowski at gmail.com
Tue Aug 25 08:34:44 CEST 2020

```P.S. Generally:

Extended problem: Are there Riesel numbers k such that |k-2^n| is a Riesel
number for every n>0 ?
By the dual Riesel conjecture, these are odd integers k such that
|k-2^m-2^n| is composite for every m>=0 and n>=0.

Similar problem: Are there Sierpinski numbers k such that k+2^n is a
Sierpinski number for every n>0 ?
By the dual Sierpinski conjecture, these are odd integers k such that
k+2^m+2^n is composite for every m>=0 and n>=0.

The next step is to combine both of these problems, but the question of
whether such Brier numbers exist is premature.

T. Ordowski
_______________________
https://en.wikipedia.org/wiki/Riesel_number#The_dual_Riesel_problem
https://en.wikipedia.org/wiki/Sierpinski_number#Dual_Sierpinski_problem
https://en.wikipedia.org/wiki/Riesel_number#Simultaneously_Riesel_and_Sierpi%C5%84ski

niedz., 23 sie 2020 o 20:34 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

>
> I have a hard problem:
>
> Are there de Polignac numbers k>1 such that
> k-2^n is a Polignac number for every 1<2^n<k
> ?
>
> These are odd integers k>3 such that
> every positive value of k-2^m-2^n is not prime
> for m>=0 and n>=0.
>
> Attention, expect big numbers!
>
> Successful searches!
>
> Thomas Ordowski
> ____________________
> https://oeis.org/A006285
>
>

```