# 質數階乘質數

pn質數階乘記作pn#。
pn# − 1是質數，對n = 2, 3, 5, 6, 13, 24, ... （OEIS中的数列A057704
pn# + 1是質數，對n = 1, 2, 3, 4, 5, 11, ...（A014545

3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209

consider any finite set of primes
(not necessarily the first n primes;
e.g. it could have been the set {3, 11, 47}),
and then went on from there to the conclusion
that at least one prime exists that is not in that set.

## 參考文獻

• A. Borning, "Some Results for ${\displaystyle k!+1}$  and ${\displaystyle 2\cdot 3\cdot 5\cdot p+1}$ " Math. Comput. 26 (1972): 567 - 570.
• Chris Caldwell, The Top Twenty: Primorial at The Prime Pages.
• Harvey Dubner, "Factorial and Primorial Primes." J. Rec. Math. 19 (1987): 197 - 203.
• Paulo Ribenboim, The New Book of Prime Number Records. New York: Springer-Verlag (1989): 4.
1. ^ Primegrid.com; official anouncement, 24 December 2010
2. ^ 本段落是譯自en:Primorial prime的第4段
3. ^ 本段是譯自en:Primorial prime的文字最後一行
4. ^ A. Borning, "Some Results for ${\displaystyle k!+1}$  and ${\displaystyle 2\cdot 3\cdot 5\cdot p+1}$ " Math. Comput. 26 (1972): 567 - 570.