A271000 Table read by rows: list of prime sextuplets (p, p+4, p+6, p+10, p+12, p+16).

7, 11, 13, 17, 19, 23, 97, 101, 103, 107, 109, 113, 16057, 16061, 16063, 16067, 16069, 16073, 19417, 19421, 19423, 19427, 19429, 19433, 43777, 43781, 43783, 43787, 43789, 43793, 1091257, 1091261, 1091263, 1091267, 1091269, 1091273, 1615837, 1615841, 1615843, 1615847, 1615849, 1615853

Offset: 1

Author

Arkadiusz Wesolowski, Jul 12 2016

Keywords

• nonn
• tabf

Comments

A prime sextuplet is a constellation of six successive primes with distance 16, and is of the form (p, p+4, p+6, p+10, p+12, p+16).

Initial members p (other than 7) of prime sextuplets are congruent to 97 (mod 210). - Ash, David, Aug 04 2017

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..5940
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 6763998516837
• Eric Weisstein's World of Mathematics, Prime Constellation
• Wikipedia, Prime quadruplet
• Index entries for primes, gaps between

Crossrefs

Cf. A022008, A270999.

Programs

Magma

lst:=[]; for p in [5..1615837 by 2] do if p le 7 xor p mod 210 eq 97 then if IsPrime(p) then t:=[c: c in [p+4..p+16] | IsPrime(c)]; if #t eq 5 then lst:=lst cat [p] cat t; end if; end if; end if; end for; lst;

Mathematica

m = {0, 4, 6, 10, 12, 16}; Union@ Flatten@ Map[# + m &, Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &]] (* Michael De Vlieger, Jul 13 2016 *)

Formula

a(6*n-5) = A022008(n).