Sierpiński Problem/Historical Note

Historical Note on Sierpiński Problem
It was proved by in $1962$ that $78\ 557$ is a Sierpiński number of the second kind.

In 1967, and  conjectured that $78\ 557$ is in fact the smallest Sierpiński number of the second kind.

To prove that this is the case, all odd positive integers smaller than $78\ 557$ are not Sierpiński numbers of the second kind.

That is, it must be shown that, for all $1 \le k \le 78\ 557$, where $k$ is odd, there exists some $n \in \Z$ such that:
 * $k 2^n + 1$

is prime.

By March 2002, there were seventeen such $k$ whose status was still unknown.

That was when the distributed computing project Seventeen or Bust was established.

Its aim was to test all these remaining seventeen numbers by exhaustively checking all values of $n$ until finding a value of $n$ for which $k 2^n + 1$ is prime.

In April 2016 the project terminated as a result of the server going down, with the resulting loss of both the server and the backups. Work continues on PrimeGrid.

As of 18 January 2017, twelve of those remaining seventeen numbers have been found to be non-Sierpiński, by establishing a value of $n$ for which $k 2^n + 1$ is prime, as follows: