Number Theory

• Jul 9th 2008, 02:10 PM
JCIR
Number Theory
disprove that there are infinitely many primes numbers p for which p+2 and p+4 are also prime numbers.
• Jul 9th 2008, 02:16 PM
ThePerfectHacker
Quote:

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?
• Jul 9th 2008, 02:16 PM
JaneBennet
Quote:

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. \$\displaystyle p=3\$ is the only prime satisfying that condition. For all other primes, either \$\displaystyle p+2\$ or \$\displaystyle p+4\$ is a multiple of 3 strictly greater than 3 and therefore cannot be prime.
• Jul 10th 2008, 12:41 PM
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".
• Jul 10th 2008, 12:49 PM
ThePerfectHacker
Quote:

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.
• Jul 10th 2008, 06:20 PM
JCIR
Sorry I did not mention I edit it
• Jul 10th 2008, 09:39 PM
Matt Westwood
Bah. Makes all the difference, that does.

RTFQ as my teacher used to say ...