A323428 Primes p such that the concatenation of p^3, p^2, p and 1 is prime.

37, 79, 967, 3181, 3463, 3607, 3643, 3691, 3931, 4657, 5227, 5419, 5569, 5953, 6217, 6379, 6529, 7417, 7603, 7753, 7759, 8527, 8887, 9049, 9277, 9343, 9679, 9829, 9871, 31723, 32323, 32983, 33151, 33601, 34039, 35227, 36529, 36913, 37189, 38329, 38707, 38749, 39097, 40123, 41149, 41479, 42073

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

All terms == 1 (mod 6).

Examples

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

Links

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

Crossrefs

Cf. A323427.

Programs

Maple

cat4:= proc(x) local t;
  t:= 10*x+1;
  t:= x^2*10^(1+ilog10(t))+t;
  x^3*10^(1+ilog10(t))+t;
end proc:
select(t -> isprime(t) and isprime(cat4(t)), [seq(i,i=1..10^5,6)]);

Mathematica

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