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).




func is_mersenne_prime(p) {
    return true if (p == 2)
    var s = 4
    var M = (2**p - 1)
    { s = powmod(s, 2, M)-2 } * (p-2)
    s == 0
}
 
Inf.times {|n|
    if (n.is_prime && is_mersenne_prime(n)) {
        say "M#{n}"
    }
}