[seqfan] The dual theorem

[Tomasz Ordowski]

Dear SeqFans,

I formulated the following conditional Theorem (two in one):

If all Sierpinski numbers are dual and all Riesel numbers are dual,
then, for any odd prime p and for any integer m >= 0,
there exists a number n >= 0 such that |(p-/+2^m)2^n+/-1| is prime.

Corollary: If p < q is a pair of twin primes,
then there are natural numbers m,n such that
the both numbers p2^m+1 and q2^n-1 are prime.

Has anyone noticed it before?

Best regards,

Thomas Ordowski
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https://en.wikipedia.org/wiki/Sierpinski_number#Dual_Sierpinski_problem
https://en.wikipedia.org/wiki/Riesel_number#The_dual_Riesel_problem