‘PRIMES AND FACTORS’ 63

directly derived from the series of natural numbers (that is,
the series of consecutive integers I, 2, 3, 4, etc.). Each odd
number can in fact be built up from two consecutive natural
numbers, whereas even numbers cannot.

Every odd number, other than 1 itself, is clearly one
greater than an even number and is therefore of the form
on 1. This is the same as n+4-(n+1) and is therefore the sum
of two consecutive natural numbers. No even number can
be formed in the same way since, for any pair of natural
numbers, one must be odd and the other even so that their
sum must also be odd.

 

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