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A116888
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Primes p that remain prime through 4 iterations of the function f(p) = p^2 + 4.
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3
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306167, 48639197, 64695713, 68252687, 87788237, 87813293, 160486967, 255974437, 283032247, 324609913, 361705873, 417684523, 449364197, 451995587, 454052213, 466037563, 536504713, 574746467, 596095613
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
p4Q[p_]:=AllTrue[NestList[#^2+4&, p, 4], PrimeQ]; Select[Prime[Range[312*10^5]], p4Q] (* Harvey P. Dale, Nov 20 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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