# 六素数

## 类型

### 六素数偶

500之下的六素数OEIS 中数列A023201A046117) 有：

(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467)

p = (117924851×587502×9001#×(587502×9001#+1)+210)×(587502×9001#−1)/35+5.[1]

9001# 是一个素数阶乘

### 六素数三元组

(7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983)

p = (84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1) / 35 + 1.[2]

### 六素数四元组

(5,11,17,23), (11,17,23,29), (41,47,53,59), (61,67,73,79), (251,257,263,269), (601,607,613,619), (641,647,653,659).

p = 411784973 · 2347# + 3301.[3]

## 参考文献

1. ^ Ken Davis, "11593 digit sexy prime pair". Retrieved 2009-05-06.
2. ^ Jens K. Andersen, "The largest known CPAP-3" 页面存档备份，存于互联网档案馆. Retrieved 2009-01-27.
3. ^ Jens K. Andersen, "Gigantic sexy and cousin primes". Retrieved 2009-01-27.
• Retrieved on 2007-02-28 (requires composite p+18 in a sexy prime triplet, but no other similar restrictions)