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.

1, 4, 6, 10, 12, 18, 22, 24, 28, 30, 40, 42, 46, 48, 52, 54, 58, 60, 66, 70, 72, 76, 78, 82, 84, 88, 90, 102, 106, 112, 114, 126, 130, 132, 136, 138, 142, 148, 150, 154, 156, 162, 168, 172, 180, 184, 186, 190, 192, 196, 198, 204, 208, 210, 220, 222, 228, 232, 238, 246, 252, 258, 262, 268, 274

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 26 2021

Keywords

• nonn
• base

Comments

All terms except 1 are even.

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

filter:= proc(m) local d,e;
   for d in numtheory:-divisors(m) do
     e:= m/d;
     if isprime(d*10^(1+ilog10(e))+e) and isprime(d+e) then return true fi
   od;
   false
end proc:
select(filter, [$1..1000]);