Problem Statement

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}

.

Calculate all Mersenne primes up to the implementation's maximum precision, or the 47th Mersenne prime   (whichever comes first).

Let's start with the solution:

val .isPrime = f .i == 2 or
    .i > 2 and not any f(.x) .i div .x, pseries 2 .. .i ^/ 2

val .isMersennePrime = f(.p) {
    if .p == 2: return true
    if not .isPrime(.p): return false

    val .mp = 2 ^ .p - 1
    for[.s=4] of 3 .. .p {
        .s = (.s ^ 2 - 2) rem .mp
    } == 0
}

writeln join " ", map f $"M\.x;", filter .isMersennePrime, series 2300