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%I #10 Nov 20 2023 11:45:04
%S 306167,48639197,64695713,68252687,87788237,87813293,160486967,
%T 255974437,283032247,324609913,361705873,417684523,449364197,
%U 451995587,454052213,466037563,536504713,574746467,596095613
%N Primes p that remain prime through 4 iterations of the function f(p) = p^2 + 4.
%e p = 306167, f(p) = 93738231893, f(f(p)) = 8786856118425842363453, f(f(f(p))) = 77208840445917661077402487029419236950083213 and the 88-digit number f(f(f(f(p)))) are all prime numbers.
%t Select[Prime[Range[9! ]],PrimeQ[ #^2+4]&&PrimeQ[(#^2+4)^2+4]&&PrimeQ[((#^2+4)^2+4)^2+4]&&PrimeQ[(((#^2+4)^2+4)^2+4)^2+4]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2010 *)
%t p4Q[p_]:=AllTrue[NestList[#^2+4&,p,4],PrimeQ]; Select[Prime[Range[312*10^5]],p4Q] (* _Harvey P. Dale_, Nov 20 2023 *)
%Y Cf. A062324, A116886, A116887, A116889.
%K nonn
%O 1,1
%A _Giovanni Resta_, Feb 27 2006
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