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:

iexpmax = 15
n=1
out=""
For iexp = 2 To iexpmax
	If iexp = 2 Then
		s = 0
	Else
		s = 4
	End If
	n = (n + 1) * 2 - 1
	For i = 1 To iexp - 2
		s = (s * s - 2) Mod n
	Next 
	If s = 0 Then
		out=out & "M" & iexp & " "
	End If
Next 
Wscript.echo out