kvkenyon
- 21
- 0
So,
Prime triplet: if p is prime, then p+2 and p+4 are also prime.
Prove that 3,5,7 is the only prime triplet.
I have figured out that
p = 2k+1, k > 1
then p+2 = 2k + 3 and p + 4 = 2k+5.
I figure there will be three cases to prove i.e.
p (prime), p + 2 (prime), p + 4 (not prime)
p (prime), p + 2 (not prime), p + 4 (prime)
p (prime), p + 2 (not prime), p +4 (not prime)
Not sure how to continue. The solution is in the book, but I just want a little hint in the right direction...and I hoped writing it out again would give me some hint. I am just starting with number theory and haven't done many proofs in my life so this feels a little tough.
Prime triplet: if p is prime, then p+2 and p+4 are also prime.
Prove that 3,5,7 is the only prime triplet.
I have figured out that
p = 2k+1, k > 1
then p+2 = 2k + 3 and p + 4 = 2k+5.
I figure there will be three cases to prove i.e.
p (prime), p + 2 (prime), p + 4 (not prime)
p (prime), p + 2 (not prime), p + 4 (prime)
p (prime), p + 2 (not prime), p +4 (not prime)
Not sure how to continue. The solution is in the book, but I just want a little hint in the right direction...and I hoped writing it out again would give me some hint. I am just starting with number theory and haven't done many proofs in my life so this feels a little tough.