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A238083 Primes p such that p^4 - p^3 + 1 is also prime.

%I A238083 #13 Jun 11 2025 16:45:00
%S A238083 67,139,337,409,577,607,631,1297,1321,1429,1459,1549,1627,2377,2557,
%T A238083 2767,2851,2917,3001,3187,3319,3499,4027,4099,4621,4861,4969,5059,
%U A238083 5431,5449,5581,5827,5857,6007,6037,6379,6481,6781,6997,7411,7927,8089,8191,8311
%N A238083 Primes p such that p^4 - p^3 + 1 is also prime.
%H A238083 K. D. Bajpai, <a href="/A238083/b238083.txt">Table of n, a(n) for n = 1..3409</a>
%e A238083 67 is in the sequence because 67 is prime and 67^4 - 67^3 + 1 = 19850359 is also prime.
%e A238083 337 is in the sequence because 337 is prime and 337^4 - 337^3 + 1 = 12859645009 is also prime.
%p A238083 KD := proc() local a,b;  a:= ithprime(n);  b:= a^4 - a^3 + 1;  if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..2000);
%t A238083 c=0; a=2; Do[k=Prime[n];  If[PrimeQ[k^4-k^3+1], c=c+1;  Print[c," ",k]],    {n,1,100000}];
%t A238083 Select[Prime[Range[1100]],PrimeQ[#^4-#^3+1]&] (* _Harvey P. Dale_, Jun 11 2025 *)
%o A238083 (PARI) isok(p) = isprime(p) && isprime(p^4 - p^3 + 1); \\ _Michel Marcus_, Feb 27 2014
%Y A238083 Cf. A000040, A237639, A237641, A237642.
%K A238083 nonn
%O A238083 1,1
%A A238083 _K. D. Bajpai_, Feb 17 2014
%E A238083 More terms from _Michel Marcus_, Feb 27 2014