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A128717 Primes that yield another prime if one adds either the sum of its digits or the product of its digits.

%I A128717 #10 Jul 12 2017 03:22:07
%S A128717 101,103,163,233,293,307,431,499,509,563,617,701,743,1009,1049,1061,
%T A128717 1087,1409,1423,1483,1489,1601,1607,1801,1867,2017,2039,2053,2273,
%U A128717 2543,2633,2903,3041,3067,3089,3449,3607,4013,4057,4079,4211,4217,4273,4507
%N A128717 Primes that yield another prime if one adds either the sum of its digits or the product of its digits.
%H A128717 Robert Israel, <a href="/A128717/b128717.txt">Table of n, a(n) for n = 1..10000</a>
%e A128717 163 + (1+6+3) = 173, 163 + 1*6*3 = 181; 173 and 181 are prime numbers.
%p A128717 filter:= proc(n) local S;
%p A128717   S:= convert(n,base,10);
%p A128717   isprime(n+convert(S,`+`)) and isprime(n+convert(S,`*`))
%p A128717 end proc:
%p A128717 A:= NULL:
%p A128717 p:= 2:
%p A128717 while p < 10000 do
%p A128717   if filter(p) then A:= A, p fi;
%p A128717   p:= nextprime(p)
%p A128717 od:
%p A128717 A; # _Robert Israel_, Jul 12 2017
%t A128717 Select[Prime[Range[500]], PrimeQ[ # + Plus @@ IntegerDigits[ # ]] && PrimeQ[ # + Times @@ IntegerDigits[ # ]] &]
%o A128717 (PARI) isok(n) = isprime(n) && (isprime(n+sumdigits(n)) && ((d=digits(n)) && isprime(n+prod(k=1, #d, d[k])))); \\ _Michel Marcus_, Jul 12 2017
%Y A128717 Cf. A048519.
%K A128717 base,easy,nonn
%O A128717 1,1
%A A128717 _J. M. Bergot_, Jun 27 2007
%E A128717 Edited, corrected and extended by _Stefan Steinerberger_, Jul 14 2007