Given any integer n, we can construct a sequence of 
at least n-1 sequential composite numbers.  That is, there is no
prime in this sequence, so that gap must be at least n-1.
<p>
Consider the number N=n!  It is easy to see that
<p>
<ul>
<li> N+2= 1*2*3*...*n + 2 = 2(1*3*4*...*n+1)
<li> N+3= 1*2*3*...*n + 3 = 3(1*2*4*...*n+1)
<li> ...
<li> N+n= 1*2*3*...*n + n = n(1*2*4*...*(n-1)+1)
</ul>