# Math Help - Number Theory

1. ## Number Theory

disprove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers.

2. Originally Posted by JCIR
Prove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers.
I think you mean: p,p+2,p+6.
If we cannot solve the rwin prime conjecture how can be possibly solve this?

3. Originally Posted by JCIR
Prove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers.
Are there? I don’t think so. $p=3$ is the only prime satisfying that condition. For all other primes, either $p+2$ or $p+4$ is a multiple of 3 strictly greater than 3 and therefore cannot be prime.

4. Probably worth pointing out that the original question was:

"DISprove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers"

NOT "Prove".

5. Originally Posted by Matt Westwood
Probably worth pointing out that the original question was:

"DISprove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers"

NOT "Prove".
That is because he edited his post. Look at what I quoted.

6. Sorry I did not mention I edit it

7. Bah. Makes all the difference, that does.

RTFQ as my teacher used to say ...