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[s0ftm0d]

If you are going to comment about the forums being flodded with crap, dont post crap yourself about brute forcing the key, IT IS NEVER GOING TO HAPPEN.  Wow you wrote a nice C program, just everyone stop about the damn key.

[azninvasion]

I know I should listen to the voiceofreason on this but I was browsing the forums and saw my thread has crept back up. That got me thinking about primes again, and I think I have come up with a solid theory on factoring primes, (at least with the smaller numbers) and want to get some input on it. I was writing this down as notes to myself but I think I should share it. I hope I don't get assassinated,   .  Well here it goes, enjoy!


If any number can be formed by the multiplication of prime numbers, than can the converse be true? That is to say, to find one prime number we must divide it by another prime?

The question is how we determine this prime number without trying n primes in order to arrive at the solution to the problem.

Suppose we were given two prime numbers. 17 and 19 and whose sum is 323.

Can we determine this without a successive try at division?

Let’s try adding 1 number to this term to end up with 324.

What is the largest divisible term?

Well we factor out the problem.

2,2,3,3,3,3

That is 2x2x3x3x3x3 = 324

Note that we took the high end of the estimate.

Now we shall take these factors and distribute them evenly

2,3,3,3,3,2

So split down the middle, we have 2,3,3 and 3,3,2

And multiply them out

18 and 18

Now since we added 1 we will add or subtract one from each side to find the primes.

Once the primes are found we will test to see if their sum is equal to the first number.

17 and 19 = 323

Does this work for much larger prime multiplication, or primes that are different?

Well let’s see.

Try 7 and 23

161
Add 1

162

Factor

2,3,3,3,3

Now we notice that the numbers are not evenly distributed which may mean that the two primes are not as close as in the previous example.

Now we have two choices

2,3,3,3,3 which will be pairs 2,3 and 3,3,3 or 2,3,3 and 3,3

We choose the first

2,3 = 6 and 3,3,3 = 27

6 is between primes 5 and 7

27 is between primes 23 and 29

We test the multiples of these 4 and we find 7 and 23 to be the correct answer equaling 161.

So the steps are simple.

1.   Add numbers to the prime to make it even, and do a prime factorization of this number.
2.   Group these prime factors into two groups.
3.   Multiply the factors in each group to arrive at two numbers.
4.   Choose a range to be tested around these numbers.
5.   From this range select the closest primes.
6.   Test those primes from the first and second groups and see if their multiples are the number being tested for.
7.   If it does not match, return to step 2 and rearrange the factors.
8.   If step 7 fails choose to subtract numbers or something.
9.   Have yourself a nice cold beer.

[VoiceOfReason]

QUOTE(azninvasion @ Jan 7 2006, 10:59 PM)

That got me thinking about primes again, and I think I have come up with a solid theory on factoring primes

Oh, factoring primes is easy. Given a prime number N, its factors are 1 and N. It's factoring composite numbers that's a problem.

QUOTE

If any number can be formed by the multiplication of prime numbers, than can the converse be true? That is to say, to find one prime number we must divide it by another prime?

I'm not quite sure what you're saying here. The idea that any number can be expressed as a unique product of primes is known as the Fundamental Theorem of Arithmetic, and yes, the converse is true: every possible product of primes results in a unique number.

QUOTE

Suppose we were given two prime numbers. 17 and 19 and whose sum is 323.

Let’s try adding 1 number to this term to end up with 324. What is the largest divisible term? Well we factor out the problem. 2,2,3,3,3,3

Okay, here's the first problem. You're trying to solve the problem of factoring 323... why should the ability to factor 324 be taken as a given? Granted, you know that by adding 1 to an odd number you'll definitely have the factor 2... but if instead of trying to factor a number with 3 digits you were trying to factor a number with 300, trying to factor the next number up isn't necessarily going to be a piece of cake.

By the way, the term for the result of a multiplication is "product", not "sum."

QUOTE

So split down the middle, we have 2,3,3 and 3,3,2 And multiply them out 18 and 18

Now since we added 1 we will add or subtract one from each side to find the primes.
Does this work for much larger prime multiplication, or primes that are different?

Nope. It doesn't necessarily even work for smaller numbers.

QUOTE

So the steps are simple.

Okay. Let's factor 57.

QUOTE

1.   Add numbers to the prime to make it even, and do a prime factorization of this number.

57+1 = 58 = 2*29

QUOTE

2.   Group these prime factors into two groups.
3.   Multiply the factors in each group to arrive at two numbers.

Okay. 2 and 29.

QUOTE

4.   Choose a range to be tested around these numbers.
5.   From this range select the closest primes.

The closest prime to 2 is 3. The closest primes to 29 are 23 and 31.

QUOTE

6.   Test those primes from the first and second groups and see if their multiples are the number being tested for.
7.   If it does not match, return to step 2 and rearrange the factors.

There's only one possible arrangement.

3 * 23 = 69, nope.
3 * 31 = 93, also nope.

QUOTE

8.   If step 7 fails choose to subtract numbers or something.
9. Have yourself a nice cold beer.

Okay, let's subtract. 57-1 = 56 = 2*2*2*7. Let's try 2*2 and 2*7. The primes around 4 are 3 and 5. The primes around 14 are 13 and 17. None of these multiply to 57. Try 2*2*2 and 7. The primes around 8 are 7 and 11, the primes around 7 are 5 and 11. Again, no dice. 2 and 2*2*7? Then we get 3 at one end, 23 and 31 on the other. Still no joy. None of these lead you to 3*19.

I agree, though, that step 9 makes sense and is a good idea.

[azninvasion]

Ah the VoiceOfReason wins over again!  Woohoo at least I know the feds won't be coming for me after all.  Yeah I didn't really take time to think about it but I suppose it wasn't an entirely lost cause.  Ah thy ponder upon thee pesterous prime, and marvel upon thy wonders. What secrets hideth thee? Wilst thou alloweth me to know? Pitty.

[raceboy404]

not to be rude, but i dont think you guys should be attcking the 360 with its own protection, lets ay they kisko demo

we can brew our own app/virus tha would burn a whol right threw all the bull and cut right down to the core and then plant a new bios, sort of like a softmod, right after it tears a wholeit would engadge on the network from your pc to the xbox and thats all i have so far,
maybe add a new app from there that is more secure

[lordvader129]

QUOTE

we can brew our own app/virus tha would burn a whol right threw all the bull and cut right down to the core and then plant a new bios, sort of like a softmod, right after it tears a wholeit would engadge on the network from your pc to the xbox and thats all i have so far,
maybe add a new app from there that is more secure

not to be rude, but do you even have the slighted clue what you are talking about here?

we cant run any homebrew apps/virus/code/anything as it wont be signed

"burning a hole through the bull" and "cutting to the core" wtf are you talkign about?

ok, so you want to plant a new bios...how? what do you think all the modchip devs are trying to do? its alot easier said than done

[raceboy404]

though the firmwere

and i wasn't talking with the kisoks disc pasficly, but like run it of somthing of that sort, maybe of a memory card of some sort

and the 360 is like a server if you think of it

u can cut right threw the secruity if u have the right program and screw around with it and make it your own

[raceboy404]

well i am sure we could definatly modd the 360 with a devolpment kit

i wounder how uyou could get a hold of one of those from M$?

how hard could it be, we are amking somthing for the 360

progress for technoligy

[lordvader129]

a dev kit will only help you write homebrew code for the 360, it wont help in hacking it (getting that code to run)

all im really getting from you is "all we need to do to hack the 360 is hack the 360" your not providing any new insight, just talking in circles

[Heet]

I like hamburgers.

[dcnigma]

i Like [IMG]http://www.bobs.com.br/images/produtos/04-double-cheeseburger_G_.jpg[IMG/]

[rooter75]

?? Hamburgers ??  I thought the discussion was about the 360 security and the private key leading into the battle of wits over prime numbers but no where did anyone bring up Lunch!

[wmadoss]

Its impossible for me to jump to the moon aswell but it doesnt hurt me trying...

Still I wouldnt spend any time on it...