20171212, 20:44  #1 
May 2017
ITALY
2×3^{2}×29 Posts 
Factorization and primality test O([log_9(N)]^3)
Factorization and primality test O([log_9(N)]^3)
https://www.academia.edu/35412746/Te...n_O_log_9_N_3_ What do you think of this? 
20171212, 21:38  #2  
"Forget I exist"
Jul 2009
Dartmouth NS
2·3·23·61 Posts 
Quote:


20171212, 21:49  #3 
May 2017
ITALY
2·3^{2}·29 Posts 
tomorrow night.
now in Italy it's late. try to understand 
20171213, 06:25  #4 
Aug 2006
5,987 Posts 
I don't read Italian. I looked at the document through Google Translate and I couldn't make heads or tails of it. Trying to work through the example I get H = 259 which doesn't give an integral K. But even if we were supposed to follow the cleanup procedure at the bottom of the second page, I don't see how any of this yields information on the factorization of the number.
But I think I should give you and your method a chance. Would you use it to factor some of these numbers, as far as it can reasonably go? Since it takes only cubic time, it should take only ~ k/3.7 seconds for a 1 GHz computer to factor the largest of these, for some constant k which you haven't revealed. Code:
64 bits: 12948110090585311979 128 bits: 191875610236165000493961741999993232961 256 bits: 104346515658715073236701578230537664345079731008268447250755923399969554554527 512 bits: 8877405418354614101337795613309676609673488389927337368943966383733022288825857519728174752110656132115481773164541042027077109668409285166080822943514087 1024 bits: 110017842535385107563795555661123030649928671048545795736220084126740077360535371108397605185633055628612036218921956452272449040580855582723250597770349258450200896920600054607239415068082852975938869913095282502118922681797947602970968857144251026353070249934660110636019299512092327020338426677133549564511 2048 bits: 32265694365222194010404357001516092548579199819041387945757267571596036749058634569094074219812846889534340995067820497901477561024599455565353002082511746648828169641181808973705035169234034211640728526085942856653459967866524633721100136389120826750971806555721953743512380362913169994078977035316885050734877880651635514708654045499243997726663832268601982453795322623327981372984678885139358313085521667255445647912968215291270713228333042612344810538357995867856503805643169118591231786654638431283960478897333710812694000748001860490290821407402203811181480383231178028186738528974827080974424570633369059334759 Last fiddled with by xilman on 20171213 at 15:07 Reason: Wrap in [code] tags to reduce window width 
20171213, 07:01  #5 
May 2017
ITALY
1012_{8} Posts 
sorry it's 3 ^ [log_9 (N)] = sqrt (N).
but I will try again 
20171213, 07:07  #6 
May 2017
ITALY
2·3^{2}·29 Posts 
I already have an exceptional idea
I'll write it in English tonight 
20171214, 11:23  #7 
May 2017
ITALY
2×3^{2}×29 Posts 
A question.
This time I do not want to be wrong about computational complexity. at each red line makes sqrt (N / 9) What is its computational complexity? thank you. 
20171214, 12:35  #8 
May 2017
ITALY
2·3^{2}·29 Posts 
then there's another one.
at each red line makes sqrt (N) What are the two computationalities? Which is the fastest? thank you 
20171214, 13:14  #9 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
14760_{8} Posts 
Alberico Lepore: Can you actually do some factorisations and prove what you are saying? Not using simple 3digit numbers, but numbers that CRGreathouse posted.
Stop pretending and start doing. 
20171214, 13:45  #10 
"Forget I exist"
Jul 2009
Dartmouth NS
8418_{10} Posts 
it would all depend on if the lines could be done in parallel for time complexity, the point being made is you have made a claim, and not supported it.

20171214, 15:03  #11 
Feb 2017
Nowhere
17CD_{16} Posts 

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