[seqfan] Problem

Tomasz Ordowski tomaszordowski at gmail.com
Tue Aug 11 18:01:54 CEST 2020

Dear readers!

Are there infinitely many primes p = k2^n+1 with k odd such that q = k+2^n
is prime?

It has to be proved that there are infinitely many primes p = (q-2^n)2^n+1
for n > 0, where q runs over all odd primes.
By the dual Sierpinski conjecture, for every odd prime q, there exists n >
0 such that it is a prime p, which ends the conditional proof.
Can you prove it unconditionally?

Best regards,

Most primes seem to have this property, but it is the illusory "law of
small numbers", I think.

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