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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.
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%I #12 Apr 27 2021 02:43:07

%S 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 84,88,90,102,106,112,114,126,130,132,136,138,142,148,150,154,156,162,

%U 168,172,180,184,186,190,192,196,198,204,208,210,220,222,228,232,238,246,252,258,262,268,274

%N 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 All terms except 1 are even.

%C Includes p-1 if p is a prime such that 10*p-9 is prime.

%H Robert Israel, <a href="/A343703/b343703.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 12 is a term because 12 = 4*3 where both 43 and 4+3=7 are prime.

%p filter:= proc(m) local d,e;

%p for d in numtheory:-divisors(m) do

%p e:= m/d;

%p if isprime(d*10^(1+ilog10(e))+e) and isprime(d+e) then return true fi

%p od;

%p false

%p end proc:

%p select(filter, [$1..1000]);

%K nonn,base

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Apr 26 2021