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).




mersenne?: function [p][
    if p=2 -> return true
    mp: dec shl 1 p
    s: 4
    loop 3..p 'i ->
        s: (sub s*s 2) % mp
    return s=0
]
 
print "Mersenne primes:"
mersennes: select 2..32 'x -> and? prime? x mersenne? x
print join.with:", " map mersennes 'm -> ~"M|m|"