Integers such that Difference with Power of 2 is always Prime/Mistake

Source Work

 * The Dictionary
 * $105$
 * $105$


 * The Dictionary
 * $105$
 * $105$

Mistake

 *  conjectured that [105] is the largest number $n$ such that the positive values of $n - 2^k$ are all prime. The only other known numbers with this property are $7$, $15$, $21$, $45$ and $75$.

Correction
First it should be noted that it should be specified that $k \ge 1$. Otherwise the statement is false: for example $7 - 2^0 = 6$ is composite.

Secondly, the list should also include $4$.