1. ## Rsa

Me and my friend were discussing cracking RSA after I mentioned an article, here, where a student made a prime number that was 6,320,430 digits long. How many bits is that? Would it be possible in a reasonible amount of time to use the same computer matrix to crack/factor RSA numbers?
//I randomly introduce the happenings of the article.
&lt;Me&gt;: The number is 6,320,430 digits long and would need 1,400 to 1,500 pages to write out. It is more than 2 million digits larger than the previous largest known prime number.
&lt;Me&gt;: largest prime number discovered.
&lt;Me&gt;: Tens of thousands of people volunteered the use of their PCs in a worldwide project that harnessed the power of 211,000 computers, in effect creating a supercomputer capable of performing 9 trillion calculations per second. Participants could run the mathematical analysis program on their computers in the background, as they worked on other tasks.
&lt;Me&gt;: In the case of Shafer's discovery, it was 2 to the 20,996,011th power minus 1. The find was independently verified by other participants in the project.
&lt;Me&gt;: (2 ^ 20996011)-1
&lt;Him&gt;: massive ass number
&lt;Me&gt;: ****ing huge
&lt;Me&gt;: Pretty neat
&lt;Me&gt;: not that it is useful.
&lt;Him&gt;: lol
&lt;Me&gt;: You'd be like here is a book.
&lt;Me&gt;: And it has the largest prime number.
&lt;Me&gt;: Then nobody would care
&lt;Me&gt;: No practical application.
&lt;Him&gt;: lol
&lt;Him&gt;: how long did it take
&lt;Me&gt;: I'll use this large as number to power the worl
&lt;Me&gt;: *world
&lt;Me&gt;: says 8yr old project
&lt;Me&gt;: so I would assume 8yrs old?
&lt;Him&gt;: i see
&lt;Me&gt;: Still
&lt;Me&gt;: 8 years, for naught.
&lt;Him&gt;: lol no, they succeeded
&lt;Me&gt;: Tell me when that number does something useful.
&lt;Me&gt;: Not yet...
&lt;Me&gt;: Yes, they accomplished their goal.
&lt;Me&gt;: But it is useless, meaningless garbage.
&lt;Me&gt;: Oh well
&lt;Him&gt;: whatever dude
&lt;Me&gt;: Well seriously.
&lt;Him&gt;: not like they could be doing something better
&lt;Me&gt;: Lol
&lt;Me&gt;: Yah they could
&lt;Me&gt;: I'll explain at school sometime how it works. [AI]
&lt;Him&gt;: and either way, 211000 comps would be overkill
&lt;Me&gt;: Not necessarily, but most likely.
&lt;Me&gt;: They could factor and RSA number.
&lt;Me&gt;: *an
&lt;Him&gt;: exactly
&lt;Me&gt;: and make money
&lt;Him&gt;: but that wasn't around when they started this project right
&lt;Him&gt;: anyway dude
&lt;Him&gt;: as soon as they did that
&lt;Me&gt;: Yes it was.
&lt;Him&gt;: couldn't rsa just use a different one
&lt;Me&gt;: RSA has been around for a while.
&lt;Me&gt;: Use a different what?
&lt;Him&gt;: number
&lt;Me&gt;: The point is that can one factor/comprimise RSA encryption at all
&lt;Me&gt;: Hell, anyone can change the number.
&lt;Him&gt;: right
&lt;Him&gt;: so if it took 211000 computers several years
&lt;Him&gt;: to crack one number
&lt;Me&gt;: The idea, as we both said, was to basically develope a new method of factoring.
&lt;Him&gt;: they just change numbers like once a month
&lt;Him&gt;: problem solved
&lt;Me&gt;: That was not the point of the challenge.
&lt;Me&gt;: Because, if all that computers on earth banded together to factor it, it would still take a long time.
&lt;Him&gt;: right
&lt;Him&gt;: dude these people didn't create a new way of factoring
&lt;Him&gt;: they just used massive computing power
&lt;Me&gt;: Look at it this way.
&lt;Me&gt;: 576 bit has not been cracked
&lt;Him&gt;: yeah
&lt;Him&gt;: why are you telling me this
&lt;Me&gt;: And this has been around for about 10 years
&lt;Him&gt;: but man, isn't this new prime number...like
&lt;Me&gt;: That it is not mere computing power, but the ability to deal with huge as numbers.
&lt;Him&gt;: several thousand bits
&lt;Me&gt;: Well..
&lt;Me&gt;: 2^big..
&lt;Me&gt;: 6,320,430
&lt;Me&gt;: I forget, but one integer is like 4 bits?
&lt;Me&gt;: something like that.
&lt;Him&gt;: yea
&lt;Him&gt;: so that's way ****ing bigger than some rsa encryption number
&lt;Me&gt;: 25281720
&lt;Me&gt;: Yes.
&lt;Me&gt;: It is however basically unusable.
&lt;Him&gt;: right...so if an rsa number is so much smaller
&lt;Me&gt;: Where as 1024-bit is able to be implimented on home PC's.
&lt;Him&gt;: why doesn't a smaller group of hackers combine to crack an rsa
&lt;Me&gt;: Better things to do? Lack of intrest? I dunno
&lt;Him&gt;: lol that's weird as hell
&lt;Him&gt;: if its that easy
&lt;Him&gt;: just combine computers
&lt;Me&gt;: Not that easy :-)
&lt;Him&gt;: dude
&lt;Him&gt;: it just takes an organizer
&lt;Him&gt;: then people willing to let their computer be used
&lt;Him&gt;: that's how easy
&lt;Me&gt;: No. You have to write software that handles multiple PC's and a bunch of other ****.
&lt;Him&gt;: RIGHT
&lt;Me&gt;: Because if it was easy, everyone would do it.
&lt;Him&gt;: AKA AN ORGANIZER
&lt;Him&gt;: you ****
&lt;Me&gt;: If RSA was easy, everyone would do it.
&lt;Me&gt;: An easy \$200K+
&lt;Him&gt;: and apparently they already have developed that software
&lt;Him&gt;: because they used it for this project
&lt;Me&gt;: For generating prime numbers.
&lt;Him&gt;: and im sure an intelligent computer programmer could write it
&lt;Him&gt;: no ****
&lt;Him&gt;: so that still can serve as a foundation
&lt;Him&gt;: and...if they can do it for making them, they can use it for factoring non primes
&lt;Him&gt;: someone made it, someone else can make it again
&lt;Me&gt;: Can I post this convo?
&lt;Me&gt;: I'm asking the probability/possabilty of it being done.
&lt;Me&gt;: ok.
&lt;Me&gt;: Cool:-)
Ok, so that was rather long.

-Cheers-

2. Trying to factor the product of that and another prime would take such an incredible amount of computing power that I cant even to develop an analogy that would do justice to it. However look into the recent changes in patent laws concering unique numbers, they're not so useless as you might think. Some people are very interested in those kinds of numbers.

-Maestr0

3. There was this estimated number of years that it would be necessary to break the RSA [I think... or was it a key lenght, but something common nowadays]. It was about 10 or 100 times as large as the estimated end of the universe [but it did not take into account technological evolution]

4. I tried to use a HP Calculator to get that number converted into binary (HP Calculators rule in running through each an every number), but it complained at 9.99*10^499...

But to figure out how many bits that is, you would convert 10^6,320,430 into 2^x, or convert it from base 10 (decimal) into base 2 (binary). To get the number of bits that is, you would have to figure out: 6320430 = log(2^x) and solve for x. (Note: It is a base 10 logarithm) Unfortunately, I'm not very good at that and my HS teachers won't show me logarithms yet, so acturally figuring out how many bits that is, I can't do it. Definately over 6 million bit in that number though, well over 6 million bits...

Edit:
A rough estimation is that this is a 18,961,290 bit key, or 2.2MB. Huge compared to 1024 bit (1 KB)...

Edit 2:
Bleh, looks like in your quote the size in bits was given -&gt; (2 ^ 20996011)-1, or 2.5MB. All that work and it was given, haha. Still, huge number. Kinda makes you wonder how many combinations a 20-200GB HDD could have...wow...

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