       Lucas Lehmer prime Mersenne test

• To: mathgroup at smc.vnet.net
• Subject: [mg52261] Lucas Lehmer prime Mersenne test
• From: Roger Bagula <tftn at earthlink.net>
• Date: Thu, 18 Nov 2004 01:45:02 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```The real problem with this test is that Mersenne
number are grossly big, but the Lucas-Lehmer test recurrence is just
bigger much too fast.
I can't get it above  n=8 in real time.
The Lucas -Lehmer numbers  are always ending in 4 and divisible by 2.

Clear[s,a,b]
(* Lucas Lehmer prime Mersenne test*)
s[n_]:=s[n]=s[n-1]^2-2
s=4
digits=8
a=Table[s[n],{n,1,8}]

{4,14,194,37634,1416317954,2005956546822746114,
4023861667741036022825635656102100994,

16191462721115671781777559070120513664958590125499158514329308740975788034}

a/2

{2,7,97,18817,708158977,1002978273411373057,
2011930833870518011412817828051050497,

8095731360557835890888779535060256832479295062749579257164654370487894017}

(* Lucas -Lehmer test applied to Mersenne numbers*)

b=Table[If[Mod[s[Prime[n]-1],2^Prime[n]-1]==0, 2^Prime[n]-1,0],{n,1,digits}]
Respectfully, Roger L. Bagula