How to resolve the algorithm Lucas-Lehmer test step by step in the Wren programming language

Problem Statement
Step by Step Solution
Sourcecode

Problem Statement

Lucas-Lehmer Test: for

{\displaystyle p}

an odd prime, the Mersenne number

− 1

{\displaystyle 2^{p}-1}

is prime if and only if

− 1

{\displaystyle 2^{p}-1}

divides

S ( p − 1 )

{\displaystyle S(p-1)}

where

S ( n + 1 )

( S ( n )

)

− 2

{\displaystyle S(n+1)=(S(n))^{2}-2}

, and

S ( 1 )

{\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:

Step by Step solution about How to resolve the algorithm Lucas-Lehmer test step by step in the Wren programming language

Source code in the wren programming language

import "./big" for BigInt
import "./math" for Int
import "io" for Stdout

var start = System.clock
var max = 19
var count = 0
var table = [521, 607, 1279, 2203, 2281, 3217, 4253, 4423]
var p  = 3 // first odd prime
var ix = 0 // index into table for larger primes
var one = BigInt.one
var two = BigInt.two
while (true) {
    var m = (BigInt.two << (p - 1)) - one
    var s = BigInt.four
    for (i in 1..p-2) s = (s.square - two) % m
    if (s.bitLength == 0) {
        count = count + 1
        System.write("M%(p) ")
        Stdout.flush()
        if (count == max) {
            System.print()
            break
        }
    }
    // obtain next odd prime or look up in table after 127
    if (p < 127) {
        while (true) {
            p = p + 2
            if (Int.isPrime(p)) break
        }
    } else {
        p = table[ix]
        ix = ix + 1
    }
}
System.print("\nTook %(System.clock - start) seconds.")


import "./gmp" for Mpz
import "./math" for Int

var start = System.clock
var max = 28
var count = 0
var table = [521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503]
var p = 3 // first odd prime
var ix = 0
var one = Mpz.one
var two = Mpz.two
var m = Mpz.new()
var s = Mpz.new()
while (true) {
    m.uiPow(2, p).sub(one)
    s.setUi(4)
    for (i in 1..p-2) s.square.sub(two).rem(m)
    if (s.isZero) {
        count = count + 1
        System.write("M%(p) ")
        if (count == max) {
            System.print()
            break
        }
    }
    // obtain next odd prime or look up in table after 127
    if (p < 127) {
        while (true) {
            p = p + 2
            if (Int.isPrime(p)) break
        }
    } else {
        p = table[ix]
        ix = ix + 1
    }
}
System.print("\nTook %(System.clock - start) seconds.")