Regarding the question of finding a sequence of non-prime natural numbers, I have consistently found an answer that states that have a 'proper' starting point, say (n+1)!+2; and then all the consecutive n numbers will be non-prime. I am unable to understand that why we need a 'proper' starting point. Is it not that any factorial (n!) will suffice as a starting point, and the number of values in the sequence will be decided by the value of n.
A case in point is an example that shows that 101!+2 is a starting point for the next 100 values, till 101!+101 being non-prime natural number. For this particular case, the logic being offered is that the value 101! and 2 have a common factor, and so on till 101! and 101.