let $n>1$ be an odd integer , i w'd like to know more about distribution of primes then i'm interesting to check enough mathematical conditions to answer my following question :
Question: When are $n$ and $n+2$ prime numbers with $n >1$ odd integer ?
EDit: for instance i find this condition : $(n-1)!$ must be not divisble by $n$ and $n+2$ i have tried with a few integers it seems works but to show it's hard for me
Thank you for any help