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).




PROGRAM LUCAS_LEHMER
  IMPLICIT NONE
 
  INTEGER, PARAMETER :: i64 = SELECTED_INT_KIND(18)
  INTEGER(i64) :: s, n
  INTEGER :: i, exponent
 
  DO exponent = 2, 31
     IF (exponent == 2) THEN
        s = 0
     ELSE
        s = 4
     END IF
     n = 2_i64**exponent - 1
     DO i = 1, exponent-2
        s = MOD(s*s - 2, n)
     END DO
     IF (s==0) WRITE(*,"(A,I0,A)") "M", exponent, " is PRIME"
  END DO
 
END PROGRAM LUCAS_LEHMER