Originally Posted by
chillerbros17 6. Prove the following theorems. State the method of proof that you are using in parts (a) and (c).
(a):Thm: The sum of two prime numbers, each greater than 2, is never a prime. Restatement: For all integers p, q, if p is a prime greater than 2 and q is a prime greater than 2, then p + q is not prime.
Proof by Contradiction (Reductio ad absurdum)
If p and q are primes greater than 2, then p and q are both odd, and may
be written p=2a+1, q=2b+1, for some positive integers a, and b.
Now suppose p+q is prime, then as it is greater than 2, it must be odd.
But:
p+q=2a+1+2b+1=2(a+b+1).
Thus p+q is divisible by 2, and hence not prime (as p+q !=2), which
is a contradiction, hence our assumption is false, and p+q is not prime.
RonL