Use Bertrand's Postulate to show that every positive integer n with n >= 7 is the sum of distinct primes.

 

I know that Bertrand's Postulate states that for every positive integer n with

n > 1, there is a prime p such that n < p < 2n.

 

So, in our case since n >= 7 > 1 we can deduce that

 

n < p < 2n

 

That's pretty much all I can say looking at the postulate itself. What else?

Suppose for a minimal counter example. N, then there is a prime in the ragen

 

N/2 to N, call it p, now think a little to get a contradiction,