[seqfan] Next Problem

[Tomasz Ordowski]

Dear readers!

Are there infinitely many primes q = k2^m-1 with k odd such that p =
|k-2^m| is prime?
2, 3, 7, 13, 17, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 79, 83, 89, 97,
103, 107, 109, 127, ...
Note that all Mersenne primes have this property in a trivial way. Find
other famous primes.
All primes q > 13 such that q == 13 (mod 20) do not have this property
(find simple proof).

Best regards,

Thomas Ordowski
_______________
Previous Problem:
Are there infinitely many primes q = k2^m+1 with k odd such that p = k+2^m
is prime?
Of course, in a trivial way, all Fermat primes have this property. Find
others yet.
All primes q > 7 such that q == 7 (mod 20) do not have this property.
Cf. https://oeis.org/history/view?seq=A332075&v=28
and https://oeis.org/history/view?seq=A332078&v=21