ensure that none of the six primes is divisible by 2, 3, 5 or 7). It is not known if there are infinitely many prime sextuplets. Once again, proving the twin prime conjecture might not necessarily prove that there are also infinitely many prime sextuplets. Also, proving that there are infinitely many prime quintuplets might not necessarily prove that there are infinitely many prime sextuplets. The Skewes number for the tuplet {p, p+4, p+6, p+10, p+12, p+16} is (). Prime k-tuples Prime quadruplets, quintuplets, and sextuplets are examples of prime constellations, and prime constellations are in turn examples of prime k-tuples. A prime constellation is a grouping of primes, with minimum prime and maximum prime , meeting the following two conditions: Not all residues modulo are represented for any prime For any given , the value of is the minimum possible More generally, a prime k-tuple occurs if the first condition but not necessarily the second condition is met. References . Classes of prime numbers Unsolved problems in mathematics