A154939 Primes p such that (p-1)*(p+1)-+p are primes.

3, 5, 11, 31, 101, 131, 149, 181, 241, 331, 419, 449, 709, 1051, 1061, 1171, 1409, 1549, 1579, 1699, 1759, 1831, 2069, 3229, 3449, 3761, 3911, 4159, 4951, 5821, 6029, 6481, 6661, 6679, 6899, 7079, 7151, 7229, 7369, 8101, 8219, 8629, 8861, 9091, 9161, 9521

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

• nonn

Comments

That is, primes p such that p^2+p-1 and p^2-p-1 are both primes: intersection of A053184 and A091567. - Michel Marcus, Jul 10 2016

Examples

			2*4=8-+3 -> primes, 4*6=24-+5 -> primes,...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A053184, A038872, A141158, A091567, A098058, A038936, A089270, A140559.

Programs

Magma

[p: p in PrimesUpTo(10000) | IsPrime(p^2+p-1) and IsPrime(p^2-p-1)]; // Vincenzo Librandi, Jul 10 2016

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*(p+1)-p]&&PrimeQ[(p-1)*(p+1)+p],AppendTo[lst,p]],{n,7!}];lst
Select[Prime[Range[1500]], And@@PrimeQ/@{#^2 - # - 1, #^2 + # - 1} &] (* Vincenzo Librandi, Jul 10 2016 *)
Select[Prime[Range[1500]],AllTrue[(#-1)(#+1)+{#,-#},PrimeQ]&] (* Harvey P. Dale, Sep 21 2023 *)