There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers I need help with this question: There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also primes.
Where should I start? what proof techniques will be useful?
Any input will be very useful to me.

If $p>3$ is a prime then reducing mod 3, one of $p+2$ and $p+4$ is $0\pmod 3$ and so is divisible by $3$. Thus, the only prime $p$ for which both $p+2$ and $p+4$ are also prime is $p=3$. 
