A prime constellation, also called a prime 
-tuple, prime 
-tuplet, or prime cluster, is a sequence of 
consecutive numbers such that the difference between the first
and last is, in some sense, the least possible. More precisely, a prime 
-tuplet is a sequence of consecutive primes
(
,
,
..., 
)
with 
,
where 
is the smallest number 
for which there exist 
integers 
, 
and, for every prime 
, not all the residues modulo 
are represented by 
, 
, ..., 
(Forbes). For each 
, this definition excludes a finite number of clusters at the
beginning of the prime number sequence. For example, (97, 101, 103, 107, 109) satisfies
the conditions of the definition of a prime 5-tuplet, but (3, 5, 7, 11, 13) does
not because all three residues modulo 3 are represented (Forbes).
A prime double with 
is of the form (
, 
) and is called a pair of twin
primes. Prime doubles of the form (
, 
) are called cousin primes,
and prime doubles of the form (
, 
) are called