# How to define a list that contains all primes less than x?

how can I define my own list in which I have all primes less than x?

Prime @ Range @ PrimePi @ x. See e.g. this question What is so special about Prime? to get an idea about possible limitations of this approach.
primeInf[x_] := Prime @ Range @ PrimePi @ x

{2, 3, 5, 7, 11, 13, 17, 19}