A227217 Primes p such that p + (product of digits of p) is prime and p - (product of digits of p) is prime.

23, 29, 83, 101, 103, 107, 109, 293, 307, 347, 349, 401, 409, 431, 439, 503, 509, 601, 607, 653, 659, 677, 701, 709, 743, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1123, 1201, 1297, 1301, 1303, 1307, 1409, 1423, 1489, 1523

Offset: 1

Author

Derek Orr, Sep 19 2013

Keywords

• nonn
• base

Comments

Intersection of A157677 and A225319.

Contains A056709. - Robert Israel, Apr 13 2015

Examples

			431 is prime, 431 + (4*3*1) = 443 is prime, and 431 - (4*3*1) = 419 is prime. So, 431 is a term in the sequence.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007954, A056709, A157677, A225319.

Programs

Maple

filter:= proc(n) local m;
  if not isprime(n) then return false fi;
  m:= convert(convert(n,base,10),`*`);
  if m = 0 then return true fi;
  isprime(n+m) and isprime(n-m)
end proc:
select(filter, [seq(2*i+1,i=5..10000)]); # Robert Israel, Apr 13 2015

Mathematica

fQ[n_] := Block[{d = IntegerDigits@ n}, PrimeQ[n + Times @@ d] && PrimeQ[n - Times @@ d]]; Select[Prime@ Range@ 250, fQ] (* Michael De Vlieger, Apr 12 2015 *)

PARI

forprime(p=1,2000,d=digits(p);P=prod(i=1,#d,d[i]);if(isprime(p+P)&&isprime(p-P),print1(p,", "))) \\ Derek Orr, Apr 10 2015

Python

from sympy import isprime, primerange
def DP(n):
    p = 1
    for i in str(n):
        p *= int(i)
    return p
for pn in primerange(1, 2000):
    dpn = DP(pn)
    if isprime(pn-dpn) and isprime(pn+dpn):
        print(pn, end=', ')
# Simplified by Derek Orr, Apr 10 2015

Sage

[p for p in primes_first_n(1000) if ((p-prod(Integer(p).digits(base=10))) in Primes() and (p+prod(Integer(p).digits(base=10))) in Primes())] # Tom Edgar, Sep 19 2013

Extensions

More terms from Derek Orr, Apr 10 2015