A229176 Primes p with nonzero digits such that p + product_of_digits and p - product_of_digits are both prime.

23, 29, 83, 293, 347, 349, 431, 439, 653, 659, 677, 743, 1123, 1297, 1423, 1489, 1523, 1657, 1867, 2239, 2377, 2459, 2467, 2543, 2579, 2663, 2753, 3163, 3253, 3271, 3329, 3457, 3461, 3581, 3691, 3727, 3833, 3947, 3967, 4129, 4253, 4297, 4423, 4567, 4957, 5323, 5381, 5651

Offset: 1

Author

Derek Orr, Sep 30 2013

Keywords

• nonn
• base
• easy

Comments

Numbers with nonzero digits in A227217; the non-degenerate cases, so to speak.

Intersection of primes with nonzero digits in A157677 and A225319.

Examples

			743 is prime.
743 - (7*4*3) = 659 is prime.
743 + (7*4*3) = 827 is prime.
So, 743 is a member of this sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A227217, A157677, A225319.

Programs

Maple

A007954 := proc(n)
    mul(d, d=convert(n, base, 10))
end proc:
isA229176 := proc(n)
    if isprime(n) and A007954(n) <> 0 then
        isprime(n+A007954(n)) and isprime(n-A007954(n))  ;
        simplify(%) ;
    else
        false;
    end if;
end proc:
for n from 1 to 10000 do
    if isA229176(n) then
        printf("%d,",n) ;
    end if;
end do:

Mathematica

id[x_] := IntegerDigits[x]; ti[x_] := Times @@ id[x]; m=5000; Select[Range[3,m,2], PrimeQ[#] && Min[id[#]] > 0 && PrimeQ[#+ti[#]] && PrimeQ[#-ti[#]]&] (* Zak Seidov, Oct 02 2013 *)
t@n_ := Block[{p = Times @@ IntegerDigits@n},
  If[p == 0, {0}, n + {-p, p}]]; Select[Prime@Range@1000,
AllTrue[t@#, PrimeQ] &] (* Hans Rudolf Widmer, Dec 13 2021 *)

PARI

forprime(p=1,10^4,d=digits(p);P=prod(i=1,#d,d[i]);if(P&&isprime(p+P)&&isprime(p-P),print1(p,", "))) \\ Derek Orr, Mar 22 2015

Python

import sympy
from sympy import isprime
def DP(n):
  p = 1
  for i in str(n):
    p *= int(i)
  return p
{print(n, end=', ') for n in range(10**4) if DP(n) and isprime(n) and isprime(n+DP(n)) and isprime(n-DP(n))}
# Simplified by Derek Orr, Mar 22 2015