A238136 Primes p such that p^4-p^3+1 and p^4-p^3-1 are also primes.

1429, 5827, 7411, 9601, 12601, 18457, 20011, 20521, 24919, 25999, 28591, 29947, 33211, 33349, 36037, 38149, 41227, 42649, 43579, 45307, 46099, 49999, 52057, 52387, 54319, 59107, 59197, 59629, 67891, 70951, 73477, 74761, 75037, 81157, 92041, 93607, 114889

Offset: 1

Author

K. D. Bajpai, Feb 18 2014

Keywords

• nonn

Examples

			1429 is in the sequence because 1429, (1429^4-1429^3+1) and (1429^4-1429^3-1) are all primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2918

Crossrefs

Cf. A000040, A237639, A237641, A237642.

Programs

Maple

KD := proc() local a, b,d; a:=ithprime(n); b:= a^4-a^3+1;d:=a^4-a^3-1; if isprime (b) and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..20000);

Mathematica

Select[Prime[Range[3000]],PrimeQ[#^4-#^3+1]&&PrimeQ[#^4-#^3-1]&]
c=0;a=2;Do[k=Prime[n];  If[PrimeQ[k^4-k^3+1] &&PrimeQ[k^4-k^3-1], c=c+1;  Print[c," ",k]],  {n,1,2000000}];
pQ[n_]:=Module[{c=n^4-n^3},AllTrue[c+{1,-1},PrimeQ]]; Select[Prime[ Range[ 11000]],pQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 19 2014 *)

PARI

s=[]; forprime(p=2, 120000, if(isprime(p^4-p^3+1) && isprime(p^4-p^3-1), s=concat(s, p))); s \\ Colin Barker, Feb 18 2014