If $ p\equiv 1\pmod 3$,then $ 2p + 1\equiv 0\pmod 3$,which is not a prime. If $ p\equiv 2\pmod 3$,then $ 4p + 1\equiv 0\pmod 3$,which is not a prime. so it's necesary $ p\equiv 0\pmod 3$ ->$ p = 3$,we have the triple $ (3,7,13)$ work.