A323427 Primes p such that the concatenation of p^2, p and 1 is prime.

2, 5, 17, 41, 89, 173, 191, 197, 293, 311, 353, 479, 491, 647, 797, 857, 887, 911, 971, 1097, 1181, 1319, 1523, 1847, 2003, 2069, 2153, 2351, 2411, 2459, 2549, 2693, 2699, 2729, 2837, 2843, 2957, 2963, 3011, 3041, 3089, 3359, 3407, 3533, 3557, 3581, 3761, 3767, 3797, 4133, 4289, 4547, 4787, 4937

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 14 2019

Keywords

• nonn
• base

Comments

All terms == 2 (mod 3).

Examples

			a(3)=17 is a term because 17 and 289171 are primes, where 17^2=289.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A323428.

Programs

Maple

cat3:= proc(x) local t;
  t:= 10*x+1;
  x^2*10^(1+ilog10(t))+t
end proc:
select(t -> isprime(t) and isprime(cat3(t)), [2,seq(i,i=5..10000,6)]);

Mathematica

ppQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n^2, n, 1]]]; Select[Prime[Range[500]], ppQ] (* Vincenzo Librandi, Jan 15 2019 *)
Select[Prime[Range[700]],PrimeQ[FromDigits[Join[IntegerDigits[#^2],IntegerDigits[#],{1}]]]&] (* Harvey P. Dale, Aug 07 2025 *)