Prime Quadruplet
A prime constellation of four successive primes with minimal distance (p, p + 2, p + 6, p + 8). The term was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The quadruplet (2, 3, 5, 7) has smaller minimal distance, but it is an exceptional special case. With the exception of (5, 7, 11, 13), a prime quadruple must be of the form (30n + 11, 30n + 13, 30n + 17, 30n + 19). The first few values of n which give prime quadruples are n = 0, 3, 6, 27, 49, 62, 69, 108, 115, ... (OEIS A014561), and the first few values of p are 5 (the exceptional case), 11, 101, 191, 821, 1481, 1871, 2081, 3251, 3461, ... (OEIS A007530). The number of prime quadruplets with largest member less than 10^1, 10^2, ..., are 1, 2, 5, 12, 38, 166, 899, 4768, ... (OEIS A050258; Nicely 1999).
