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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A237639, A237641, A237642.

Sequence in context: A321036 A094230 A353080 * A060364 A243834 A124087

Adjacent sequences: A238133 A238134 A238135 * A238137 A238138 A238139

Keyword

nonn

Author

K. D. Bajpai, Feb 18 2014

Status

approved