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Re: How do I do very big integer computing by Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg115373] Re: How do I do very big integer computing by Mathematica?
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sun, 9 Jan 2011 02:19:18 -0500 (EST)

----- Original Message -----
> From: "a boy" <avvboy at gmail.com>
> To: mathgroup at smc.vnet.net
> Sent: Saturday, January 8, 2011 2:37:07 AM
> Subject: [mg115335] How do I do very big integer computing by Mathematica?
> 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?

Not exactly certain what you want to do from that description. But something that might help is to interleave Mod[] operations provided the modulus is not too large for Mathematica.

Daniel Lichtblau
Wolfram Research