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?

$p = 59 \implies k = 2p + 1 = 119$. Neither $6k+1 = 715$ nor $6k-1 = 713$ is prime. Some other counter examples are:
59
          83
          89
         103
         109
         137
         139
         149
         151
         163
         193
         239
         269
         281
