lets break this in simple terms
first x cant be 1
now for all y given (
if there is some z such that x=y*z then y=1 or y= x)
now take x=4, then for all y(
take y=1, then some z is 4 i.e 4=1*4 so T->T T
take y=4, then some z is 1 i.e. 4=4*1 so T->T T
take y=2,then some z is 2 i.e.4=2*2 so T->F F as y != 2 or x(4) so it is not true for all y hence x= 4 is eliminated in fact all composite will be false and only prime no will be true for all y because for e.g 7=1*7 or 7=7*1 both cases satisfy this for all y and other than 1 and 7 you cant find any other factors .
so x represents all prime no and 1 is not prime as it is already removed at start.