Sum of Sequence of Alternating Positive and Negative Factorials being Prime/Mistake
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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): $19$