From previous posts in this thread we see that all of these numbers have a neighbour divisible by 6.
This can either be P-1 or P+1, Q-1 or Q+1 and N-1 or N+1
Taking the square root of N we get a number which is between P and Q, and closest to the lower of the two
So how do we find out which primes P and Q are? The mathematical problem here is that we can't build a numerical method which is designed to reduce certain difference.
So we're not directly going to look for P and Q, we're going to look for the 6-neighbours.
Suppose we'd have 17 * 11, we have the neighbours 18 and 12, dividing by 6 we get 3 and 2.
3*2 = 6, so the idea is to find 6 as a starting point.
6 * 36 = 216, 18*12 = 216, 17*11 = 187. 180 is the first factor of 36 smaller than 187.
In this case, 180 is our first starting point. We divide by 36 to get 5, we then try to find two factors making 5 (which we don't find)
If we desing this function propperly we do get a minimum and a maximum closest to 187.
Next we must determine our new starting point, which is in this case 180+36 = 216. We then found the neighbours, we then found the primes.
Determining the starting point is the part I'm still stuck with but hey, I'm not spending all my time on this thing.
Only thing I know is that the difference by the first and final start points is caused by the distance between P and Q!
The routine which looks for two factors of the starting point / 36 can be speeded up because we're looking for neighbours, so if we don't find the neighbours, we will find a difference.
Suppose starting point x (already divided by 36):
suppose f1 * f2 == x.
for the difference we determine the closest to the prime by (( f1 +/- 1 ) * 6) * (( f2 +/- 1) * 6)
If we have this minimal diffrence m and maximum difference M, the looping factor (i.e.) can be lowered by (M - m) / 36.
I have tried more like lowering with m / 36, sqrt(m) etc.
This decreasion number speeds up finding of the neighbours, so we're not stuck with the same PQ-problem in a different outfit!
Because the function is designed to do a numerical determination of P and Q, the function can be made very fast.
In one of my test cases, My program only needed 6 iterations to determine 641 * 13 (or something like that).
You're right that I should provide proof, and I'm not doing slashdot for Karma, but for fun. I have previously posted a story on prime-numbers before on slashdot, but the article was rejected.
I'm now trying to find contacts in the mathematical world, and at this moment, I don't know how and where to publish the source code, I don't have a home-page right now, I should make one because explaining the algorithmn needs some more information.
I Posted a C++ source code to one of the PGP organizations for cracking the prime-number problem yesterday (keep you posted on their reply), if I'm as close as I think, we'll see a new era of encryption technology soon.
Darwin's evolution says that the strongest species will survive, one of the newest theories herein is that all new species must get socially accepted to survive, i.e. one can be a strong specimen, but you can be destroyed by the surrounding world.
I think much of this is happening in the free speech world of the internet. Regard the internet as an immature thing right now, we're growing, we're fighting hacks, kiddy porn and racism, we're fighting it ourselves or via our gouvernment.
The attitude / subjects of speech are species on the internet, in the end, the unaccecpted will be eleminated to a safe level.
Some sceptisism exists on the new Crusoe chip. And although Transmeta has to fight all sorts of enemies, I still do wish them the best luck with their chip.
IBM surely is going to manufacture the thing, so they have one of the big guys on their side, let the ball roll!
According to the ZD anchor desk there exists some sceptisism on the Transmeta success.
OK, Linus is our hero, but you know that the best ideas usually don't have the best success. It's usually the worst ideas who have great success like: any Microsoft product, SQL, Intel x86 processors.
I wish Transmeta the best of luck though, I reckon Crusoe could even penetrate the PC market in the end.
Some forsee a fortunate future for Linux in combination with Be.
As many think that Linux for the desktop isn't much of a winner, one could think of solutions where Linux runs the server, and BeOs runs the desktop.
This isn't such a bad idea, isn't Apple Mr User-friendly, Mr GUI?
The founder of Be was an ex-employee (and one of you will ofcourse submit his name!) of Apple.
I myself find Be very interesting, have never seen it, but if I owed the money, I'd purchase an IMac, install Be, and network the Linux-Box / Be desktop together...
Re:Damn still no Open Source Beer
on
Free Be
·
· Score: 1
Maybe we should ask Heineken to sponsor GNU-projects
Slashdot Mirror
Did they benchmark on long-run stability?
There's a Federal Bank in Britain who run Win NT networks, they shut it down once a month so that the system goes down when it's planned!
I can't believe that Win2K performs better than Red Hat, they could like even benchmark DOS 1.0 here...
My English skills aren't that bad, but I was at work and had little time. Read my newest post to get an idea of how I'm looking for the primes
Take P and Q being prime, the product is N.
From previous posts in this thread we see that all of these numbers have a neighbour divisible by 6.
This can either be P-1 or P+1, Q-1 or Q+1 and N-1 or N+1
Taking the square root of N we get a number which is between P and Q, and closest to the lower of the two
So how do we find out which primes P and Q are? The mathematical problem here is that we can't build a numerical method which is designed to reduce certain difference.
So we're not directly going to look for P and Q, we're going to look for the 6-neighbours.
Suppose we'd have 17 * 11, we have the neighbours 18 and 12, dividing by 6 we get 3 and 2.
3*2 = 6, so the idea is to find 6 as a starting point.
6 * 36 = 216, 18*12 = 216, 17*11 = 187. 180 is the first factor of 36 smaller than 187.
In this case, 180 is our first starting point. We divide by 36 to get 5, we then try to find two factors making 5 (which we don't find)
If we desing this function propperly we do get a minimum and a maximum closest to 187.
Next we must determine our new starting point, which is in this case 180+36 = 216. We then found the neighbours, we then found the primes.
Determining the starting point is the part I'm still stuck with but hey, I'm not spending all my time on this thing.
Only thing I know is that the difference by the first and final start points is caused by the distance between P and Q!
The routine which looks for two factors of the starting point / 36 can be speeded up because we're looking for neighbours, so if we don't find the neighbours, we will find a difference.
Suppose starting point x (already divided by 36):
suppose f1 * f2 == x.
for the difference we determine the closest to the prime by (( f1 +/- 1 ) * 6) * (( f2 +/- 1) * 6)
If we have this minimal diffrence m and maximum difference M, the looping factor (i.e.) can be lowered by (M - m) / 36.
I have tried more like lowering with m / 36, sqrt(m) etc.
This decreasion number speeds up finding of the neighbours, so we're not stuck with the same PQ-problem in a different outfit!
Because the function is designed to do a numerical determination of P and Q, the function can be made very fast.
In one of my test cases, My program only needed 6 iterations to determine 641 * 13 (or something like that).
The numbers:
a0 a1 a2 a3 a4 a5 a6
a1 = a0+1, a2=a0+2 etc.
a0 - divisible by 6
a1 - odd
a2 - divisible by 2
a3 - divisible by 3
a4 - divisible by 2
a5 - odd
a6 - divisible by 6
a1 and a5 are either composite prime numbers, or they're prime.
so any P*Q = N ===> all P,Q and N are either any a1 or a5...
I'll maybe post some more later, I'm now going home from work...
I haven't shown anything yet... but that 1 and 5 is a very important propperty
And that's exactly wat this is all about!!!
And if you now the whole story, you can think of an algorithmn which solves the prime-number problem in RSA!!!
17*11 = 187
187-1 = 186 ==> 186 / 6 = 31... 186 MOD 6 == 0
voila!
Take any product P*Q = N(P and Q both prime)
This is always true:
(N+1) MOD 6 == 0 or
(N-1) MOD 6 == 0
-- check it, and keep yer karma points!
YOU CAN USE THIS FOR A NUMMERICAL DETERMINATION!
I'm now trying to find contacts in the mathematical world, and at this moment, I don't know how and where to publish the source code, I don't have a home-page right now, I should make one because explaining the algorithmn needs some more information.
I Posted a C++ source code to one of the PGP organizations for cracking the prime-number problem yesterday (keep you posted on their reply), if I'm as close as I think, we'll see a new era of encryption technology soon.
I think much of this is happening in the free speech world of the internet. Regard the internet as an immature thing right now, we're growing, we're fighting hacks, kiddy porn and racism, we're fighting it ourselves or via our gouvernment.
The attitude / subjects of speech are species on the internet, in the end, the unaccecpted will be eleminated to a safe level.
I meant enemies
IBM surely is going to manufacture the thing, so they have one of the big guys on their side, let the ball roll!
OK, Linus is our hero, but you know that the best ideas usually don't have the best success. It's usually the worst ideas who have great success like: any Microsoft product, SQL, Intel x86 processors.
I wish Transmeta the best of luck though, I reckon Crusoe could even penetrate the PC market in the end.
zes uur precies
Supposedly they'll present a design of the chip, not a real silicon thing.
I hope too that CNN broadcasts pictures on this, we don't have ZDTV here in Europe, and I can't watch via internet.
*emptyness*
Didn't their Court-behaviour crush that anyways?
Imagine writing an ERP system for the Nintendo, this is cool stuff. So let's do a PostGresSQL DB on the Nintendo, it rocks! :)
As many think that Linux for the desktop isn't much of a winner, one could think of solutions where Linux runs the server, and BeOs runs the desktop.
This isn't such a bad idea, isn't Apple Mr User-friendly, Mr GUI?
The founder of Be was an ex-employee (and one of you will ofcourse submit his name!) of Apple.
I myself find Be very interesting, have never seen it, but if I owed the money, I'd purchase an IMac, install Be, and network the Linux-Box / Be desktop together...
Maybe we should ask Heineken to sponsor GNU-projects
The English language has a problem with the word 'free'. It either means 'free' as in no charge, or it means 'free' as in freedom.
The Open Source License protects the software legally, this used to be a 'Free-source-license'. So the 'Free' word made a lot of confusion.
Advocates used metaphors like 'free-beer' and 'freedom' to explain what was meant by this 'free' word.
Today we talk about Open-source, such that the 'free' word doesn't confuse anymore.
The 'free-beer' expression is inherited by the legal problems Open Source used to have, it means gratis, no-charge etc.
Just curiousity: Do you live on this site?
Would you like to try this expand-or-die-thing?
Taking 'evasive' actions in an extreme hostile atmosphere? Did you know that Martian storms make our own hurricanes look like a little breeze!
'Unsuitable' terrain? How we're gonna find terrain that's suitable? With the manned probes we sent before?
shut up loser
I rest my case!
(By the way, this should be a story found on ZDNet, but I couldn't find it).