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