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).




 
using Primes
 
function getmersenneprimes(n)
    t1 = time()
    count = 0
    i = 2
    while(n > count)
        if(isprime(i) && ismersenneprime(2^BigInt(i) - 1))
            println("M$i, cumulative time elapsed: $(time() - t1) seconds")
            count += 1
        end
        i += 1
    end
end
 
getmersenneprimes(50)
 