How do I prove a 4000 digit number is prime??
 

I have one 31-digit factor from a number of the k*2^n+1 type where n=~7300,

How do I check if the "Co-factor" is prime, it ends in ....1162049124129

Thanks

Not to get everyone excited I don't think the co-factor is prime, but how do I check or continue to find factors of this "co-factor"...

I'll try

[url]http://www.alpertron.com.ar/ECM.HTM[/url]

You can put use raw interger numbers... in addition to equations.

It will do a Rabin probabilistic prime check

Lately, I've found [url=http://www.ellipsa.net/index.html]Primo[/url], which seems to be a relatively fast primalty proving program for numbers of no special form.
Unfortunately, 4000 digits will most likely still take [url=http://www.ellipsa.net/primo/top20.html]several weeks or even months[/url].

It seems like Jens Franke et. al have a [url=http://www.ellipsa.net/primo/record.html#03]distributed primalty proving program[/url], though.

[QUOTE=Mystwalker]Lately, I've found [url=http://www.ellipsa.net/index.html]Primo[/url], which seems to be a relatively fast primalty proving program for numbers of no special form.
Unfortunately, 4000 digits will most likely still take [url=http://www.ellipsa.net/primo/top20.html]several weeks or even months[/url].

It seems like Jens Franke et. al have a [url=http://www.ellipsa.net/primo/record.html#03]distributed primalty proving program[/url], though.[/QUOTE]I went to the website and discovered some comments about the US, Canadian, and Japanese patent laws being so overly patent-happy(my word) that the writer fears getting sued. The thing is, even though he says the usage is forbidden the download proceeds without a hitch.

Am I breaking any laws if I use this software?

Edit: I'm a US resident in Arkansas.