A190792 Primes p=prime(i) such that prime(i+3)-prime(i)=12.

17, 19, 29, 31, 41, 59, 61, 67, 71, 127, 227, 229, 269, 271, 347, 431, 607, 641, 1009, 1091, 1277, 1279, 1289, 1291, 1427, 1447, 1487, 1597, 1601, 1607, 1609, 1657, 1777, 1861, 1987, 2129, 2131, 2339, 2371, 2377, 2381, 2539, 2677, 2687, 2707, 2789, 2791

Offset: 1

Author

Zak Seidov, May 20 2011

Keywords

• nonn
• easy

Comments

Minimal distance between prime(i) and prime(i+3) is 12 if all three consecutive prime gaps are different.

There are 6 possible consecutive prime gap configurations:

{2,4,6}, {2,6,4}, {4,2,6}, {4,6,2}, {6,2,4}, and {6,4,2}.

Least prime quartets with such gap configurations are:

{17,19,23,29}->{2,4,6}

{29,31,37,41}->{2,6,4}

{67,71,73,79}->{4,2,6}

{19,23,29,31}->{4,6,2}

{1601,1607,1609,1613}->{6,2,4}

{31,37,41,43}->{6,4,2}.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031165, A078847.

Programs

Magma

[NthPrime(i): i in [2..60000] | NthPrime(i+3)-NthPrime(i) eq 12];  // _Bruno Berselli-, May 20 2011

Mathematica

p = Prime[Range[1000]]; First /@ Select[Partition[p, 4, 1], Last[#] - First[#] == 12 &] (* T. D. Noe, May 23 2011 *)

PARI

is(n)=if(!isprime(n), return(0)); my(p=nextprime(n+1),q); if(p-n>6, return(0)); q=nextprime(p+1); q-n<11 && nextprime(q+1)-n==12 \\ Charles R Greathouse IV, Sep 14 2015