How do I do very big integer computing by Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg115335] How do I do very big integer computing by Mathematica?*From*: a boy <avvboy at gmail.com>*Date*: Sat, 8 Jan 2011 03:37:07 -0500 (EST)

I'm going to search big Fibonacci prime numbers. I think there is a simple primality test algorithm for Fibonacci number, like Lucas=96 Lehmer primality test for 2^n-1 . I'm lazy and don't want to write many codes. So i want to ask: p=43,112,609; s[0]=4; s[n_]:=s[n-1]^2-4 pt=Mod[s[p-2], 2^p-1]==0 how do I compute s[43,112,609-2] directly? It seems the largest integer in M~ is 2^32^32, isn't it?