A160858 Primes p such that p^3-p^2-1 and p^3-p^2+1 are prime.

2, 3, 13, 541, 859, 1279, 1459, 1951, 2239, 2971, 3181, 4003, 4129, 6343, 7393, 8053, 9043, 9463, 10501, 10831, 12433, 14083, 14731, 15073, 15991, 16603, 17443, 17491, 17761, 18493, 19861, 20173, 20323, 20929, 21391, 22963, 23071

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 29 2009

Keywords

• nonn

Examples

			3^3-3^2=27-9=18-+1=primes
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subset of A045331.

Programs

Mathematica

lst={};Do[p=Prime[n];a=p^2;b=p^3;c=b-a;If[PrimeQ[c-1]&&PrimeQ[c+1],AppendTo[lst,p]],{n,2*7!}];lst
Select[Prime[Range[3000]],AllTrue[#^3-#^2+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 20 2018 *)

PARI

forprime(p=2,1e6,if(isprime(p^3-p^2-1)&&isprime(p^3-p^2+1),print1(p",")))

Extensions

Program, cross-reference, and editing by Charles R Greathouse IV, Nov 02 2009