A prime triplet is a prime constellation of the form (
, 
,
), (
, 
,
), etc. Hardy and Wright (1979, p. 5)
conjecture, and it seems almost certain to be true, that there are infinitely many
prime triplets of the form (
, 
,
) and (
, 
,
).
| triplet | Sloane | first member |
( ,  ,
 ) | A022004 | 5, 11, 17, 41, 101, 107, ... |
( ,  ,  ) | A046134 | 3, 5, 11, 29, 59, 71, 101, ... |
( ,  ,  ) | A046135 | 5, 11, 17, 29, 41, 59, 71, ... |
( ,  ,  ) | A022005 | 7, 13, 37, 67, 97, 103, ... |
( ,  ,  ) | A046136 | 3, 7, 13, 19, 37, 43, 79, ... |
( ,  ,  ) | A046137 | 7, 19, 67, 97, 127, 229, ... |
( ,  ,  ) | A046138 | 5, 11, 23, 53, 101, 131, ... |
( ,  ,  ) | A046139 | 7, 13, 31, 37, 61, 73, 97, ... |
( ,  ,  ) | A023241 | 5, 7, 11, 17, 31, 41, 47, ... |
( ,  ,  ) | A046141 | 5, 11, 29, 59, 71, 89, 101, ... |
As of Apr. 2019, the largest known prime triplet of the form 
has smallest member
 |
and each of its three members has 
decimal digits.
-Tuplets."