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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Subset of A045331.

Sequence in context: A132484 A376060 A258357 * A062648 A094003 A119987

Adjacent sequences: A160855 A160856 A160857 * A160859 A160860 A160861

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 29 2009

Extensions

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

Status

approved