6x±1: 5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,55,59,61,65,67,71,73,77,79,83,85,89,91,95,97,

101,103,107,109,113,115,119,121,125,127,131,133,137,139,143,145,149,151,155,157,161,163,167,169,173,175,179,181,185,187,191,193,197,199,203,205,209,211

Is this just a poor sieve for odd-number pairs or is there something more going on within the factors of 6x±1?