Lucas-Lehmer Test:

for 



p


{\displaystyle p}

 an odd prime, the Mersenne number 




2

p


−
1


{\displaystyle 2^{p}-1}

 is prime if and only if 




2

p


−
1


{\displaystyle 2^{p}-1}

 divides 



S
(
p
−
1
)


{\displaystyle S(p-1)}

 where 



S
(
n
+
1
)
=
(
S
(
n
)

)

2


−
2


{\displaystyle S(n+1)=(S(n))^{2}-2}

, and 



S
(
1
)
=
4


{\displaystyle S(1)=4}

.



Task

Calculate all Mersenne primes up to the implementation's
maximum precision, or the 47th Mersenne prime   (whichever comes first).




defmodule LucasLehmer do
  use Bitwise
  def test do
    for p <- 2..1300, p==2 or s(bsl(1,p)-1, p-1)==0, do: IO.write "M#{p} "
  end
 
  defp s(mp, 1), do: rem(4, mp)
  defp s(mp, n) do
    x = s(mp, n-1)
    rem(x*x-2, mp)
  end
end
 
LucasLehmer.test