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Numbers n such that n^4+1 and (n+2)^4+1 are both prime.
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%I #10 Sep 08 2022 08:46:04

%S 2,4,46,54,80,88,140,276,492,554,566,582,730,758,786,798,912,928,1142,

%T 1150,1200,1236,1404,1540,1552,1610,1644,1650,1932,1942,2044,2102,

%U 2204,2222,2224,2238,2254,2374,2436,2486,2510,2640,2674,2698,2732,2734,3244,3286

%N Numbers n such that n^4+1 and (n+2)^4+1 are both prime.

%H Vincenzo Librandi, <a href="/A217795/b217795.txt">Table of n, a(n) for n = 1..1000</a>

%e 4 is in the sequence because 4^4+1 = 257 and 6^4+1 = 1297 are both prime.

%p for n from 0 by 2 to 3500 do: if type(n^4+1,prime)=true and type((n+2)^4+1,prime)=true then printf(`%d, `,n):else fi:od:

%t lst={}; Do[p=n^4+1; q=(n+2)^4+1;If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 0, 3000}];lst

%t Select[Range[3500],AllTrue[{#^4+1,(#+2)^4+1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 29 2015 *)

%o (Magma) [n: n in [0..3300] | IsPrime(n^4 + 1) and IsPrime((n + 2)^4 + 1)]; // _Vincenzo Librandi_, Oct 13 2012

%Y Cf. A000068, A002523, A037896.

%K nonn,easy

%O 1,1

%A _Michel Lagneau_, Oct 12 2012