%I
%S 17,19,29,31,41,59,61,67,71,127,227,229,269,271,347,431,607,641,1009,
%T 1091,1277,1279,1289,1291,1427,1447,1487,1597,1601,1607,1609,1657,
%U 1777,1861,1987,2129,2131,2339,2371,2377,2381,2539,2677,2687,2707,2789,2791
%N Primes p=prime(i) such that prime(i+3)prime(i)=12.
%C Minimal distance between prime(i) and prime(i+3) is 12 if all three consecutive prime gaps are different.
%C There are 6 possible consecutive prime gap configurations:
%C {2,4,6}, {2,6,4}, {4,2,6}, {4,6,2}, {6,2,4}, and {6,4,2}.
%C Least prime quartets with such gap configurations are:
%C {17,19,23,29}>{2,4,6}
%C {29,31,37,41}>{2,6,4}
%C {67,71,73,79}>{4,2,6}
%C {19,23,29,31}>{4,6,2}
%C {1601,1607,1609,1613}>{6,2,4}
%C {31,37,41,43}>{6,4,2}.
%H Charles R Greathouse IV, <a href="/A190792/b190792.txt">Table of n, a(n) for n = 1..10000</a>
%t p = Prime[Range[1000]]; First /@ Select[Partition[p, 4, 1], Last[#]  First[#] == 12 &] (* _T. D. Noe_, May 23 2011 *)
%o (MAGMA) [NthPrime(i): i in [2..60000]  NthPrime(i+3)NthPrime(i) eq 12]; // Bruno Berselli, May 20 2011
%o (PARI) is(n)=if(!isprime(n), return(0)); my(p=nextprime(n+1),q); if(pn>6, return(0)); q=nextprime(p+1); qn<11 && nextprime(q+1)n==12 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A078847.
%K nonn,easy
%O 1,1
%A _Zak Seidov_, May 20 2011
