A323428 - OEIS

%I #11 Jan 15 2019 12:13:39

%S 37,79,967,3181,3463,3607,3643,3691,3931,4657,5227,5419,5569,5953,

%T 6217,6379,6529,7417,7603,7753,7759,8527,8887,9049,9277,9343,9679,

%U 9829,9871,31723,32323,32983,33151,33601,34039,35227,36529,36913,37189,38329,38707,38749,39097,40123,41149,41479,42073

%N Primes p such that the concatenation of p^3, p^2, p and 1 is prime.

%C All terms == 1 (mod 6).

%H Robert Israel, <a href="/A323428/b323428.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=967 is a term because 967 is prime and 9042310639350899671 is prime, where 967^3=904231063 and 967^2=935089.

%p cat4:= proc(x) local t;

%p   t:= 10*x+1;

%p   t:= x^2*10^(1+ilog10(t))+t;

%p   x^3*10^(1+ilog10(t))+t;

%p end proc:

%p select(t -> isprime(t) and isprime(cat4(t)), [seq(i,i=1..10^5,6)]);

%t pppQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n^3, n^2, n, 1]]]; Select[Prime[Range[4500]], pppQ] (* _Vincenzo Librandi_, Jan 15 2019 *)

%Y Cf. A323427.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 14 2019