Definition:Sierpiński Number of the Second Kind/Sequence

Definition

The sequence of known Sierpiński numbers of the second kind starts:

$78\ 557, \ 271\ 129, \ 271\ 577, \ 322\ 523, \ 327\ 739, \ 482\ 719, \ 575\ 041, \ 603\ 713, \ 903\ 983, \ 934\ 909, \ 965\ 431, \ \ldots$

This sequence is A076336 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

It has been conjectured that $78 \, 557$ is the smallest Sierpiński number of the second kind.

Although it was proved by John Selfridge in $1962$ that $78 \, 557$ is Sierpiński, there are still some numbers smaller than that whose status is uncertain.

Sources

• Weisstein, Eric W. "Sierpiński Number of the Second Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html