Monday, September 10, 2007
JSH: Surrogate factoring, implementation
It is increasingly clear to me that mathematicians STILL will not follow mathematical proof so I'm working now on the implementation of surrogate factoring to give the demonstration that so many of you clamor for.
That is slow going though as my solution is to have my surrogate factoring code call itself to factor its surrogates that are being used to factor the target.
But even that can do ok, as here's some output where I'm just kind of typing numbers in at random:
Factors:
( 131 )( 2531 )( 10957 )( 40357 )( 682739052250888729441 )
Product: 100098765678976543215788865435214249
In coming is 100098765678976543215788865435214249
Surrogate factorization data for target:
Surrogates factored : 36
Surrogates not factored : 106
Factored fuel percentage: 25%
Data about all surrogates including those from recursions:
Factored fuel : 116306
Fuel not factored: 206
Factored fuel percentage: 99%
Processing time: 62172
Number of digits: 36
bitLength=117
------------------------------------
So with a really big number most of the surrogates aren't getting factored as the program just kind of tosses them and moves on if it can't factor the surrogate, but still it took only 142 surrogates total, though luckily for me there were small prime factors with one big one, so it's not that grand of a demo but I'm getting there.
With recursive calls trying to factor surrogates the program factored 116,306 but was unable to factor 206, which includes the 106 of the surrogates for the target T.
If I can get the program to factor more of its own surrogates when the size increases then I can put in an RSA challenge number.
Slow going but given time I can probably get a program together that ends all debate and simply post a factorization of an RSA challenge number.
And then watch how the math community worldwide reacts.
Posters on sci.math have begged for a demonstration against RSA and it looks like it is coming.
Maybe irony demands that I post the solution if I achieve that goal, on this newsgroup, where so many of you have begged for it.
I think the newsgroup deserves it and the aftermath.
[A reply to someone who suggested that James might want to use the Factor software.]
My invention.
My math.
Your funeral if I win this thing.
No more debates. No more stupid taunts from people like you.
I shut you down. Period.
[A reply to someone who suggested that James had nothing.]
The editors of the Bulletin of the AMS agreed with you.
So there is no way anyone can blame me for releasing the full theory, correct?
I will do so, Wednesday.
[A reply to his own assertion that if he can get the program to factor more of its own surrogates when the size increases, then he can put in an RSA challenge number.]
Maybe. Here's current output where I'm looking at increasing k, as there is some pattern to this where increasing k is part of the solution.
Begin program output:
n_min=-4095
n_max=511
n_max-n_min=4606
Surrogate factorization: factored? Yes.
( 227961623 )
Product: 227961623
Surrogate factorization: factored? Yes.
( 2 )( 228404723 )
Product: 456809446
Surrogate factorization: factored? Yes.
( 3^2 )( 11^2 )( 277 )( 2273 )
Product: 685657269
Surrogate factorization: factored? Yes.
( 2^2 )( 228626273 )
Product: 914505092
Surrogate factorization: factored? Yes.
( 5 )( 1237 )( 184859 )
Product: 1143352915
Surrogate factorization: factored? Yes.
( 2 )( 3 )( 439 )( 520957 )
Product: 1372200738
Surrogate factorization: factored? Yes.
( 7 )( 23 )( 47 )( 211583 )
Product: 1601048561
Surrogate factorization: factored? Yes.
( 2^6 )( 19 )( 733 )( 2053 )
Product: 1829896384
Surrogate factorization: factored? Yes.
( 3 )( 13 )( 1151 )( 45863 )
Product: 2058744207
Surrogate factorization: factored? Yes.
( 2 )( 5 )( 181 )( 1263863 )
Product: 2287592030
Surrogate factorization: factored? Yes.
( 2516439853 )
Product: 2516439853
Surrogate factorization: factored? Yes.
( 2^2 )( 3^2 )( 41 )( 61 )( 30491 )
Product: 2745287676
Surrogate factorization: factored? Yes.
( 17 )( 1399 )( 125053 )
Product: 2974135499
Surrogate factorization: factored? Yes.
( 2 )( 7 )( 11 )( 20798593 )
Product: 3202983322
Surrogate factorization: factored? Yes.
( 3 )( 5 )( 29 )( 1021 )( 7727 )
Product: 3431831145
Surrogate factorization: factored? Yes.
( 2^3 )( 269 )( 1701059 )
Product: 3660678968
Surrogate factorization: factored? Yes.
( 3889526791 )
Product: 3889526791
Surrogate factorization: factored? Yes.
( 2 )( 3 )( 31 )( 37 )( 598427 )
Product: 4118374614
Surrogate factorization: factored? Yes.
( 521 )( 577 )( 14461 )
Product: 4347222437
Surrogate factorization: factored? Yes.
( 2^2 )( 5 )( 79 )( 2896247 )
Product: 4576070260
Surrogate factorization: factored? Yes.
( 3^3 )( 7 )( 43 )( 199 )( 2971 )
Product: 4804918083
Surrogate factorization: factored? Yes.
( 2 )( 13 )( 83 )( 2332607 )
Product: 5033765906
Surrogate factorization: factored? Yes.
( 11257 )( 467497 )
Product: 5262613729
Surrogate factorization: factored? Yes.
( 2^4 )( 3 )( 1069 )( 107021 )
Product: 5491461552
Number factored.
k=+/-684602
n=-4072
n_max=511
Total all combinations: 22518
Time: 293
Time/combination: 0.01301181277200462
Surrogate:
( 2^4 )( 3 )( 1069 )( 107021 )
Product: 5491461552
Surrogate combinations checked: 233
Initial Factorization:
f_1=12757
f_2=17939
Now checking its factors…
Success!
Factors:
( 3 )( 12757 )( 17939 )
Product: 686543469
In coming is 686543469
Surrogate factorization data for target:
Surrogates factored : 24
Surrogates not factored : 0
Factored fuel percentage: 100%
Data about all surrogates including those from recursions:
Factored fuel : 2177
Fuel not factored: 851
Factored fuel percentage: 71%
Processing time: 625
Number of digits: 9
bitLength=30
--------------------End program output-------------------------
What's interesting here is that all the surrogates were factored and it took 24 to factor with 233 combinations checked, which are what other posters call "probes".
The combinations are when the program takes a factorization of a particular surrogate and loops through every way to factor it into two factors and checks them with the equations derived from the surrogate factoring congruences.
Now I did that run after doing a previous run on the same number with a smaller range for the n's, and it took 1893 combinations, and 151 surrogates.
The difference here was using k = 2*floor(sqrt(9T)) for the first example versus k = 2*floor(sqrt(8T)) for the second.
Now I'd like to remind that I believe there is every evidence that this approach to factoring is worth considering but that the mathematical community to date is WILLFULLY choosing to act like this is nothing, and thereby saying to the world that it is research that should not concern world leaders, investors around the world and ordinary citizens who care about their countries and the way of life.
If they turn out to be wrong then they should necessarily face the consequences.
With expert status comes expert responsibility.
I say that because I have quite a bit of research now where I believe that narrow minded members of the math community choose to deliberately ignore it, in order to protect the current status quo.
If so, then they should have to pay a price if their strategy is hugely wrong.
Proof of concept.
And proof of contradiction from a mathematical community that pushed headlines when another factoring technique managed just barely to factor—15.
Your community if full of fools.
Now see if you can get a major news organization to care about what you do so easily as you did in the past.
You people come after me and you shred yourselves.
The news organizations of the world are learning that you decide on a whim what you choose to think is important, so one factoring technique manages to factor 15, and you promote it like it's a mega event.
And I demonstrate factoring much bigger numbers and you say it's nothing.
What will your community do when you are just talking to yourselves and no major news organization will report anything you claim?
I suspect you will do what you're doing now, continue to go insane.
As the mathematical community slowly goes insane and I watch, you think the rest of the world can't notice as well—because you're going insane.
That is slow going though as my solution is to have my surrogate factoring code call itself to factor its surrogates that are being used to factor the target.
But even that can do ok, as here's some output where I'm just kind of typing numbers in at random:
Factors:
( 131 )( 2531 )( 10957 )( 40357 )( 682739052250888729441 )
Product: 100098765678976543215788865435214249
In coming is 100098765678976543215788865435214249
Surrogate factorization data for target:
Surrogates factored : 36
Surrogates not factored : 106
Factored fuel percentage: 25%
Data about all surrogates including those from recursions:
Factored fuel : 116306
Fuel not factored: 206
Factored fuel percentage: 99%
Processing time: 62172
Number of digits: 36
bitLength=117
------------------------------------
So with a really big number most of the surrogates aren't getting factored as the program just kind of tosses them and moves on if it can't factor the surrogate, but still it took only 142 surrogates total, though luckily for me there were small prime factors with one big one, so it's not that grand of a demo but I'm getting there.
With recursive calls trying to factor surrogates the program factored 116,306 but was unable to factor 206, which includes the 106 of the surrogates for the target T.
If I can get the program to factor more of its own surrogates when the size increases then I can put in an RSA challenge number.
Slow going but given time I can probably get a program together that ends all debate and simply post a factorization of an RSA challenge number.
And then watch how the math community worldwide reacts.
Posters on sci.math have begged for a demonstration against RSA and it looks like it is coming.
Maybe irony demands that I post the solution if I achieve that goal, on this newsgroup, where so many of you have begged for it.
I think the newsgroup deserves it and the aftermath.
[A reply to someone who suggested that James might want to use the Factor software.]
My invention.
My math.
Your funeral if I win this thing.
No more debates. No more stupid taunts from people like you.
I shut you down. Period.
[A reply to someone who suggested that James had nothing.]
The editors of the Bulletin of the AMS agreed with you.
So there is no way anyone can blame me for releasing the full theory, correct?
I will do so, Wednesday.
[A reply to his own assertion that if he can get the program to factor more of its own surrogates when the size increases, then he can put in an RSA challenge number.]
Maybe. Here's current output where I'm looking at increasing k, as there is some pattern to this where increasing k is part of the solution.
Begin program output:
n_min=-4095
n_max=511
n_max-n_min=4606
Surrogate factorization: factored? Yes.
( 227961623 )
Product: 227961623
Surrogate factorization: factored? Yes.
( 2 )( 228404723 )
Product: 456809446
Surrogate factorization: factored? Yes.
( 3^2 )( 11^2 )( 277 )( 2273 )
Product: 685657269
Surrogate factorization: factored? Yes.
( 2^2 )( 228626273 )
Product: 914505092
Surrogate factorization: factored? Yes.
( 5 )( 1237 )( 184859 )
Product: 1143352915
Surrogate factorization: factored? Yes.
( 2 )( 3 )( 439 )( 520957 )
Product: 1372200738
Surrogate factorization: factored? Yes.
( 7 )( 23 )( 47 )( 211583 )
Product: 1601048561
Surrogate factorization: factored? Yes.
( 2^6 )( 19 )( 733 )( 2053 )
Product: 1829896384
Surrogate factorization: factored? Yes.
( 3 )( 13 )( 1151 )( 45863 )
Product: 2058744207
Surrogate factorization: factored? Yes.
( 2 )( 5 )( 181 )( 1263863 )
Product: 2287592030
Surrogate factorization: factored? Yes.
( 2516439853 )
Product: 2516439853
Surrogate factorization: factored? Yes.
( 2^2 )( 3^2 )( 41 )( 61 )( 30491 )
Product: 2745287676
Surrogate factorization: factored? Yes.
( 17 )( 1399 )( 125053 )
Product: 2974135499
Surrogate factorization: factored? Yes.
( 2 )( 7 )( 11 )( 20798593 )
Product: 3202983322
Surrogate factorization: factored? Yes.
( 3 )( 5 )( 29 )( 1021 )( 7727 )
Product: 3431831145
Surrogate factorization: factored? Yes.
( 2^3 )( 269 )( 1701059 )
Product: 3660678968
Surrogate factorization: factored? Yes.
( 3889526791 )
Product: 3889526791
Surrogate factorization: factored? Yes.
( 2 )( 3 )( 31 )( 37 )( 598427 )
Product: 4118374614
Surrogate factorization: factored? Yes.
( 521 )( 577 )( 14461 )
Product: 4347222437
Surrogate factorization: factored? Yes.
( 2^2 )( 5 )( 79 )( 2896247 )
Product: 4576070260
Surrogate factorization: factored? Yes.
( 3^3 )( 7 )( 43 )( 199 )( 2971 )
Product: 4804918083
Surrogate factorization: factored? Yes.
( 2 )( 13 )( 83 )( 2332607 )
Product: 5033765906
Surrogate factorization: factored? Yes.
( 11257 )( 467497 )
Product: 5262613729
Surrogate factorization: factored? Yes.
( 2^4 )( 3 )( 1069 )( 107021 )
Product: 5491461552
Number factored.
k=+/-684602
n=-4072
n_max=511
Total all combinations: 22518
Time: 293
Time/combination: 0.01301181277200462
Surrogate:
( 2^4 )( 3 )( 1069 )( 107021 )
Product: 5491461552
Surrogate combinations checked: 233
Initial Factorization:
f_1=12757
f_2=17939
Now checking its factors…
Success!
Factors:
( 3 )( 12757 )( 17939 )
Product: 686543469
In coming is 686543469
Surrogate factorization data for target:
Surrogates factored : 24
Surrogates not factored : 0
Factored fuel percentage: 100%
Data about all surrogates including those from recursions:
Factored fuel : 2177
Fuel not factored: 851
Factored fuel percentage: 71%
Processing time: 625
Number of digits: 9
bitLength=30
--------------------End program output-------------------------
What's interesting here is that all the surrogates were factored and it took 24 to factor with 233 combinations checked, which are what other posters call "probes".
The combinations are when the program takes a factorization of a particular surrogate and loops through every way to factor it into two factors and checks them with the equations derived from the surrogate factoring congruences.
Now I did that run after doing a previous run on the same number with a smaller range for the n's, and it took 1893 combinations, and 151 surrogates.
The difference here was using k = 2*floor(sqrt(9T)) for the first example versus k = 2*floor(sqrt(8T)) for the second.
Now I'd like to remind that I believe there is every evidence that this approach to factoring is worth considering but that the mathematical community to date is WILLFULLY choosing to act like this is nothing, and thereby saying to the world that it is research that should not concern world leaders, investors around the world and ordinary citizens who care about their countries and the way of life.
If they turn out to be wrong then they should necessarily face the consequences.
With expert status comes expert responsibility.
I say that because I have quite a bit of research now where I believe that narrow minded members of the math community choose to deliberately ignore it, in order to protect the current status quo.
If so, then they should have to pay a price if their strategy is hugely wrong.
Proof of concept.
And proof of contradiction from a mathematical community that pushed headlines when another factoring technique managed just barely to factor—15.
Your community if full of fools.
Now see if you can get a major news organization to care about what you do so easily as you did in the past.
You people come after me and you shred yourselves.
The news organizations of the world are learning that you decide on a whim what you choose to think is important, so one factoring technique manages to factor 15, and you promote it like it's a mega event.
And I demonstrate factoring much bigger numbers and you say it's nothing.
What will your community do when you are just talking to yourselves and no major news organization will report anything you claim?
I suspect you will do what you're doing now, continue to go insane.
As the mathematical community slowly goes insane and I watch, you think the rest of the world can't notice as well—because you're going insane.
# posted by James Harris @ 20:48 
