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A235982
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Numbers n of the form p^4 + 1 (for prime p) such that n^4 + 1 is also prime.
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2
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82, 38950082, 47458322, 131079602, 1982119442, 25856961602, 58120048562, 602425897922, 1053022816562, 1267247769842, 3491998578722, 7181161893362, 7759350084722, 10756569837842, 16948379819282, 28424689653362, 33122338550402, 36562351115762, 50897394646082
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OFFSET
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1,1
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COMMENTS
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All numbers are congruent to 2 mod 20.
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LINKS
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EXAMPLE
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10756569837842 = 1811^4 + 1 (1811 is prime) and 10756569837842^4 + 1 is prime, so 10756569837842 is a member of this sequence.
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MATHEMATICA
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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 *)
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PROG
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(Python)
import sympy
from sympy import isprime
{print(n**4+1) for n in range(10000) if isprime(n) if isprime((n**4+1)**4+1)}
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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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