find all natural nos n auch that n(n+1)(n+2)(n+3) has exactly 3 prime divisors.

 

seems to never hold true for 'sufficiently' large nos. many small n satisfy.

small n's are more likely because the concentration of primes is greater at small n.

 

as n increases, you'll need more large primes. and as large primes are sparsely concentrated the chance of any particular n having 3 prime divisors becomes less likely. i'm sure with enough searching you'll find plenty though.