Outwardly, this may seem a bit difficult to accomplish, but think about the sequence
Here, we can easily show that .
Since and trivially, then it must be the case that and all one hundred terms of the sequence are composite.
In fact, this can be generalized. To find consecutive composite numbers, the same line of reasoning can be used to show that the sequence contains all composite numbers. This also naively bounds the rate of growth of the spread of primes to be at least for the spread of primes..