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A343703 Numbers k such that k=x*y for some x and y such that x+y and the concatenation of x and y are both prime.

%I A343703 #12 Apr 27 2021 02:43:07
%S A343703 1,4,6,10,12,18,22,24,28,30,40,42,46,48,52,54,58,60,66,70,72,76,78,82,
%T A343703 84,88,90,102,106,112,114,126,130,132,136,138,142,148,150,154,156,162,
%U A343703 168,172,180,184,186,190,192,196,198,204,208,210,220,222,228,232,238,246,252,258,262,268,274
%N A343703 Numbers k such that k=x*y for some x and y such that x+y and the concatenation of x and y are both prime.
%C A343703 All terms except 1 are even.
%C A343703 Includes p-1 if p is a prime such that 10*p-9 is prime.
%H A343703 Robert Israel, <a href="/A343703/b343703.txt">Table of n, a(n) for n = 1..10000</a>
%e A343703 a(5) = 12 is a term because 12 = 4*3 where both 43 and 4+3=7 are prime.
%p A343703 filter:= proc(m) local d,e;
%p A343703    for d in numtheory:-divisors(m) do
%p A343703      e:= m/d;
%p A343703      if isprime(d*10^(1+ilog10(e))+e) and isprime(d+e) then return true fi
%p A343703    od;
%p A343703    false
%p A343703 end proc:
%p A343703 select(filter, [$1..1000]);
%K A343703 nonn,base
%O A343703 1,2
%A A343703 _J. M. Bergot_ and _Robert Israel_, Apr 26 2021