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
>>
>>
>>

```

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