A173629 Numbers k with property that p = 10k + 1, p^3 + 6, p^3 + 12 and p^3 + 18 are all prime.
235, 699, 4945, 19375, 22378, 76978, 77143, 77934, 88021, 90387, 106441, 106623, 138319, 144715, 174562, 189837, 197455, 199951, 201541, 202542, 243583, 247642, 269583, 280591, 353104, 367912, 418389, 449980, 456376, 484704, 504727, 506923
Offset: 1
Keywords
Crossrefs
a(n) = (A173628(n) - 1)/10.
Programs
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Magma
[n: n in [0..600000]| IsPrime(10*n+1) and IsPrime(1000*n^3+300*n^2 +30*n+7) and IsPrime(1000*n^3+300*n^2+30*n+13) and IsPrime(1000*n^3+ 300*n^2+30*n+19)] // Vincenzo Librandi, Dec 13 2010
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Mathematica
okQ[n_]:=Module[{n3=n^3},And@@PrimeQ[{n3+6,n3+12,n3+18}]] Floor[#/10]&/@Select[Select[Table[10n+1,{n,0,600000}],PrimeQ],okQ] (* Harvey P. Dale, Dec 16 2010 *)