\begin{definition}[Definition:Sierpiński Number of the Second Kind/Sequence]
The  sequence of known '''Sierpiński numbers of the second kind''' starts:
:$78\ 557, \ 271\ 129, \ 271\ 577, \ 322\ 523, \ 327\ 739, \ 482\ 719, \ 575\ 041, \ 603\ 713, \ 903\ 983, \ 934\ 909, \ 965\ 431, \ \ldots$
{{OEIS|A076336}}
It has been conjectured that $78 \, 557$ is the smallest Sierpiński number of the second kind.
Although it was proved by {{AuthorRef|John Lewis Selfridge|John Selfridge}} in $1962$ that $78 \, 557$ is Sierpiński, there are still some numbers smaller than that whose status is uncertain.
\end{definition}