Assume there are a finite number of primes. Let p be the largest prime. Then 3p+2 is an odd number > 5, so it must be expressible as the sum of 3 primes. But si

Assume there are a finite number of primes. Let p be the largest prime. Then 3p+2 is an odd number > 5, so it must be expressible as the sum of 3 primes. But since p is the largest prime, the sum of 3 primes can never be larger than 3p, contradiction.