A088483 Primes p such that p^2+p-1 and p^2+p+1 are twin primes.

2, 3, 5, 41, 59, 89, 101, 131, 743, 761, 1193, 2411, 2663, 2729, 3011, 3221, 3251, 3449, 4751, 6173, 6599, 6833, 7229, 8669, 9059, 9323, 9521, 9719, 9743, 10151, 10781, 11549, 11933, 12143, 12251, 12473, 12641, 13553, 13613, 14939, 15569, 16301

Offset: 1

Author

Pierre CAMI, Nov 09 2003

Keywords

• nonn

Comments

Also primes in A155173 = Short leg A of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs... - Vladimir Joseph Stephan Orlovsky, Jan 21 2009

All terms >3 are congruent to 5 modulo 6. - Zak Seidov, Mar 21 2014

Intersection of A000040 and A088485. - Danny Rorabaugh, May 15 2017

Examples

			a(7) = 101: 101*101 + 101 - 1 = 10301, 10301 and 10303 twin primes.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A088484, A088485.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p1=p*p+p-1]&&PrimeQ[p1+2],AppendTo[lst,p]],{n,2*7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 21 2009 *)
Select[Prime[Range[2000]],AllTrue[#^2+#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Feb 22 2023 *)

PARI

forprime(p=2,1e5,if(isprime(p^2+p-1)&&isprime(p^2+p+1),print1(p", "))) \\ Charles R Greathouse IV, Dec 27 2011