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

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$19$

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 David Wells: Curious and Interesting Numbers (2nd ed.), 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 On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008) extends this list considerably, and reports that the list has been proven to be finite.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $19$