For any k>0 there is an N(k)
such that for all n>N applies: In the interval [n,2n] there exists
(at least) one k-tuple of prime numbers
(prime constellations).

I checked it for:

k=2 (twins), N=6,

k=3 (triples), N=21,

k=4 (quadruples), N=414,

each with n up to 20000