2014/036) Demonstrate that prime numbers (except for the "2"), can only be expressed as the sum of two consecutive natural numbers.

let the number of numbers be n and 1st number a+1

then sum of numbers= an + n(n+1)/2

it is integer

 if n is odd (n+1)/2 is integer so the expression  is divisible by n

if n is even an and n(n+1)/2 is divisible by n/2

so if n > 2 and odd it is not prime as divisible by n

if n > 2 and even it is divisible by n/2(which is >= 2) so not prime