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Numbers n such that n, 2*n+1, 3*n+2, 4*n+3, 5*n+4 and 6*n+7 are primes.
1

%I #8 Jun 19 2024 16:35:49

%S 5,89,154769,209039,513239,658349,709589,1265549,1527629,1698569,

%T 1937459,2022389,2397449,3486839,5053949,5642369,5917259,7057769,

%U 7685459,8071139,8424569,9864839,10366439,11673899,12327629,12935999

%N Numbers n such that n, 2*n+1, 3*n+2, 4*n+3, 5*n+4 and 6*n+7 are primes.

%H Vincenzo Librandi, <a href="/A174591/b174591.txt">Table of n, a(n) for n = 1..186</a>

%t Select[Prime[Range[1000000]], And@@PrimeQ/@{2 # + 1, 3 # + 2, 4 # + 3, 5 # + 4, 6 # + 7} &] (* _Vincenzo Librandi_, Sep 24 2014 *)

%t Select[Prime[Range[10^6]],AllTrue[{2#+1,3#+2,4#+3,5#+4,6#+7},PrimeQ]&] (* _Harvey P. Dale_, Jun 19 2024 *)

%o (Magma) [n: n in [1..15000000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2) and IsPrime(4*n+3) and IsPrime(5*n+4) and IsPrime(6*n+7)];

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Mar 23 2010