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%I #25 Feb 28 2022 17:57:02
%S 2,3,5,7,113,131,151,311,2111,11113,11117,11131,11171,11311,111121,
%T 111211,112111,1111151,1111711,1117111,1171111,111111113,111111131,
%U 111113111,115111111,131111111,1111111121,1111211111,1121111111,11111111113,11111111131,11113111111
%N Multiplicative and additive primes: primes where the product and sum of digits are also prime.
%C Any term of this sequence has one prime digit and all other digits are 1. - _Sean A. Irvine_, Apr 17 2021
%H Alois P. Heinz, <a href="/A046713/b046713.txt">Table of n, a(n) for n = 1..1000</a>
%t d[n_]:=IntegerDigits[n]; t={}; Do[p=Prime[n]; If[PrimeQ[Plus@@(x=d[p])]&&PrimeQ[Times@@x],AppendTo[t,p]],{n,2*10^5}]; t (* _Jayanta Basu_, May 18 2013 *)
%t Select[Prime[Range[5033*10^5]],AllTrue[{Total[IntegerDigits[ #]],Times@@ IntegerDigits[ #]},PrimeQ]&] (* or -- much faster *) Select[Union[ Flatten[ Table[FromDigits/@Permutations[PadRight[{p},n,1]],{p,{2,3,5,7}},{n,11}]]],AllTrue[{#,Total[ IntegerDigits[#]],Times@@ IntegerDigits[ #]},PrimeQ]&] (* _Harvey P. Dale_, Feb 28 2022 *)
%Y Intersection of A028834, A028842, and A000040.
%Y Intersection of A046703 and A046704.
%K nonn,base
%O 1,1
%A _Felice Russo_
%E More terms from _Harvey P. Dale_, Aug 23 2000
%E Corrected by _Jud McCranie_, Jan 03 2001
%E Edited by _Charles R Greathouse IV_, Aug 02 2010
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