**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

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