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

*To*: mathgroup at smc.vnet.net*Subject*: [mg115395] Re: How do I do very big integer computing by Mathematica?*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 10 Jan 2011 02:36:13 -0500 (EST)*References*: <igbnia$hho$1@smc.vnet.net>

In[1]:= PowerMod[2, 2^64, 1342352] Out[1]= 963840 works great :) On 09.01.2011 08:19, a boy wrote: > I asked how to do very-big-integer computing. For example: > Mod[2^2^64,1342352] > It's pity, this code causes overflow! > is there some funtions like this: StringMod["111...111","345"] > > On Sun, Jan 9, 2011 at 8:17 AM, Daniel Lichtblau<danl at wolfram.com> wrote: > >> >> ----- 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: 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 >> >> >>