A conjecture about the form of some prime numbers Let $k$ be an odd number of the form $k=2p+1$ ,where $p$ denote any prime number, then it is true that for each number $k$ at least one of $6k-1$, $6k+1$ gives a prime number.
Can someone prove or disprove this statement?

You got confused with your quantifiers, but if your conjecture is what I guess it is, then the first five counterexamples are $p=$ 59,83,89,103,109.
