A prime quadruplet is a set of four prime numbers, $p, p + 2, p + 6, p + 8$ . In most cases, $p + 4$ is a multiple of 15. The only quadruplet for which this is not the case is 5, 7, 11, 13, which overlaps with the quadruplet 11, 13, 17, 19. Sometimes 2, 3, 5, 7 is referred to as a prime quadruplet.

If the twin prime conjecture is ever proven it is possible that it might neither prove nor disprove the prime quadruplet conjecture.

The sum of the reciprocals of the members of the prime quadruplets is Brun's constant for prime quadruplets, $B_4 \approx 0.87058838$ .