It is well-known in high-level mathematics that:
(Euler-Mascheroni Constant)
(Meissel-Mertens Constant)
Is there a divergent series such that:
If so, can it be generalized to ?
Is there a meaningful infinite set , such that
diverges ~
Like maybe let ~prime,~p\equiv1\mod4\}" alt="A=\{p\in\mathbb{N}~prime,~p\equiv1\mod4\}" />
But, for all I know, that could converge. (I know that if ~prime,~p+2~also~prime\}" alt="A=\{p~prime,~p+2~also~prime\}" />, then the series does converge.)
Actually, now that I think about it, that sum must converge, because
EDIT: Although, the above calculation seems to imply that if we let ~prime,~p\equiv3\mod4\}" alt="B=\{p~prime,~p\equiv3\mod4\}" /> then diverges.