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).




s = 0
DO exponent = 2, 31
  IF(exponent > 2) s = 4
  n = 2^exponent - 1
  DO i = 1, exponent-2
    s = MOD(s*s - 2, n)
  ENDDO
  IF(s == 0) WRITE(Messagebox) 'M', exponent, ' is prime;', n
ENDDO
 
END