# 歐幾里得數

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.

3, 7, 31, 211, 2311, 30031, 510511 （OEIS中的数列A006862）.
 未解決的數學問題：是否存在無限多個歐幾里得素數?

E6 = 13# + 1 = 30031 = 59 × 509是第一個歐幾里得合數

## 參考文獻

1. ^ Michael Hardy and Catherine Woodgold, "Prime Simplicity", Mathematical Intelligencer, volume 31, number 4, fall 2009, pages 44–52.
2. ^ A. Borning, "有些結果${\displaystyle k!+1}$ and ${\displaystyle 2\cdot 3\cdot 5\cdot p+1}$" Math. Comput. 26 (1972): 567 - 570.
3. ^ 本段是譯自en:Euclid number的文字第2段
4. ^