Find 20 consecutive composite numbers.

Consider the following

Theorem:

There are arbitrarily large gaps in the series of primes. Stated otherwise, given any positive integer k, there exist k consecutive composite integers.

Proof:

Consider the integers

, and so on, so forth

Every one of these is composite because j divides , if .

Hence, for example, 20 consecutive composite numbers are as follows:

, , , , .

More later,

Nalin Pithwa