# [seqfan] New dual set

Tomasz Ordowski tomaszordowski at gmail.com
Thu Aug 20 14:12:40 CEST 2020

Dear readers,

I have two interesting conjectures:

(a) There are odd numbers k such that |k-2^m+2^n| is composite for every
m>=0 and n>=0.
(b) There are odd numbers k such that |(k-/+2^m)2^n+/-1| is composite for
every m>=0 and n>=0.

By the dual Sierpinski and by the dual Riesel conjecture, the sets of these
numbers k are equal.

To find candidates for such numbers k, let's limit m and n to 2^m<k and
2^n<k.
The covering-set system will be used to verify the candidates.  Good luck!

Best regards,

Thomas Ordowski
_______________________
<https://en.wikipedia.org/wiki/Sierpinski_number#Dual_Sierpinski_problem>
https://en.wikipedia.org/wiki/Sierpinski_number#Dual_Sierpinski_problem
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/Covering_set

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