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

%I A323427 #17 Aug 07 2025 15:27:16
%S A323427 2,5,17,41,89,173,191,197,293,311,353,479,491,647,797,857,887,911,971,
%T A323427 1097,1181,1319,1523,1847,2003,2069,2153,2351,2411,2459,2549,2693,
%U A323427 2699,2729,2837,2843,2957,2963,3011,3041,3089,3359,3407,3533,3557,3581,3761,3767,3797,4133,4289,4547,4787,4937
%N A323427 Primes p such that the concatenation of p^2, p and 1 is prime.
%C A323427 All terms == 2 (mod 3).
%H A323427 Robert Israel, <a href="/A323427/b323427.txt">Table of n, a(n) for n = 1..10000</a>
%e A323427 a(3)=17 is a term because 17 and 289171 are primes, where 17^2=289.
%p A323427 cat3:= proc(x) local t;
%p A323427   t:= 10*x+1;
%p A323427   x^2*10^(1+ilog10(t))+t
%p A323427 end proc:
%p A323427 select(t -> isprime(t) and isprime(cat3(t)), [2,seq(i,i=5..10000,6)]);
%t A323427 ppQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n^2, n, 1]]]; Select[Prime[Range[500]], ppQ] (* _Vincenzo Librandi_, Jan 15 2019 *)
%t A323427 Select[Prime[Range[700]],PrimeQ[FromDigits[Join[IntegerDigits[#^2],IntegerDigits[#],{1}]]]&] (* _Harvey P. Dale_, Aug 07 2025 *)
%Y A323427 Cf. A323428.
%K A323427 nonn,base
%O A323427 1,1
%A A323427 _J. M. Bergot_ and _Robert Israel_, Jan 14 2019