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Originally posted by tauristercus
I've had a very long interest (obsession ?) with prime numbers, especially with recovering the initial 2 prime numbers that were multiplied together to give a product. e.g 7 x 11 = 77.
In other words, if you were only given the product 77 and were asked to determine the original 2 primes used to create this value, you'd basically have little choice except to use "brute force" techniques and hammer away at this 77 value with every prime number that was smaller than the square root of this value ... eventually finding that 7 is one prime factor and therefore 11 is the other prime factor.
It's taken me a number of years but I've successfully derived an alternative method of retrieving the prime factors of ANY product that is supplied. It's already been succesfully tested on small digit length products and succesfully extracts both primes in each case. The only remaining issue I have is the subject of this thread, and if it can be resolved, will make this an incredibly useful tool for extracting primes from ANY size product and will do this extremely quickly.
Isn't it freaking obvious...destroy the worlds means of data encryption...making it obsolete...none of your data will be safe...mwahahaha...
what will you do with that program once it's done ?
this multiplication of 2 big prime numbers is an encoder isn't it ?
what will you do with that program once it's done ?
Originally posted by SpookyVince
An interesting point to notice though...
Everytime you reach one of your solutions (i.e. finding a and b so that for the 2 integer values of x the equation = 0), we can notice that the two roots (x1 and x2) multplied give b.
Similarly, we can notice that a is x1+x2...
Examples with your examples:
- a=225, b=3150 gives x1=15 and x2=210. x1*x2 = 15*210 = 3150, x1+x2 = 225
- starting with 23 and 1866, we have a=167 and b=1860, x1=12 and x2=155, and 12*155=1860 and 12+155 = 167
It seems to work everytime.
Originally posted by xmaddness
Here is the best paper I could find on a quick algorithm to do what you are looking for. It doesn't need to be O(n^2) and in fact can be reduced to O(nlog^3n), making the calculations much faster.
www.computer.org...
Originally posted by tauristercus
I don't have a rigorous proof yet to conclusively state that "this process will always yield an integer value eventually" but I have run thousands of small scale tests using relatively small prime numbers to create the product ... and in each and every case, integer roots have ALWAYS been generated eventually.
Originally posted by Byrd
...and you could always just do it in reverse; start from the answer and see what the equation comes out to be.
Are you certain? If you're doing it via calculator or computer, you will ALWAYS run into buffer overflows which will cause it to round the number to only 10 decimal places.
I had thought of that as well but he seems reluctant to explain exactly WHY he is picking coefficients in a particular way and so would it be valid for this purpose? If all were shared then perhaps some useful constraints would emerge.