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%I #15 Jul 08 2019 12:00:25
%S 82,38950082,47458322,131079602,1982119442,25856961602,58120048562,
%T 602425897922,1053022816562,1267247769842,3491998578722,7181161893362,
%U 7759350084722,10756569837842,16948379819282,28424689653362,33122338550402,36562351115762,50897394646082
%N Numbers n of the form p^4 + 1 (for prime p) such that n^4 + 1 is also prime.
%C All numbers are congruent to 2 mod 20.
%e 10756569837842 = 1811^4 + 1 (1811 is prime) and 10756569837842^4 + 1 is prime, so 10756569837842 is a member of this sequence.
%t nfp4Q[n_]:=Module[{p=Surd[n-1,4]},AllTrue[{p,n^4+1},PrimeQ]]; Select[ Range[ 2700]^4+ 1,nfp4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 08 2019 *)
%o (Python)
%o import sympy
%o from sympy import isprime
%o {print(n**4+1) for n in range(10000) if isprime(n) if isprime((n**4+1)**4+1)}
%Y Cf. A002523, A000068.
%K nonn
%O 1,1
%A _Derek Orr_, Jan 17 2014
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