Sum of Sequence of Alternating Positive and Negative Factorials being Prime/Mistake

Source Work

 * The Dictionary
 * $19$
 * $19$

Mistake

 * $19! - 18! + 17! - 16! + \dotsb + 1$ is prime. The only other numbers with this property are $3$, $4$, $5$, $6$, $7$, $8$, $10$ and $15$.

Correction
What should have been said is:
 * ... The only other known numbers with this property are ...

In, this entry has been expanded to read:
 *  ... The only other known numbers with this property are $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $41$, $59$, $61$, $105$ and $160$.

It is also worth pointing out that extends this list considerably, and reports that the list has been proven to be finite.