On 5 Jan, 02:39, David Bernier <david...@videotron.ca> wrote: > On 01/04/2013 12:07 PM, David Bernier wrote:> On 01/04/2013 10:46 AM, JT wrote: > >> On 4 Jan, 15:46, JT<jonas.thornv...@gmail.com> wrote: > >>> I remember doing this in a tentamen during my education in information > >>> theory beleiving what i did was binary sort but my teacher informed me > >>> it wasn't so what is it. > > [...] > > > > > > > > > > >> heap, what is the difference betwee a heap and a tree?). > > >> So what you think about the mix using this kind of sort for counting > >> in values, and then quicksort to sort the none null tree nodes by > >> sizes. > > > Oops.. below is about factoring. The best algorithms > > have been getting better since Maurice Kraitchik's [1920s] > > improvement on Fermat's method of expressing a number > > as a difference of squares, n = a^2 - b^2, so > > n = (a-b) (a+b). > > > There's a very good article called "A Tale of Two Sieves" > > by Carl Pomerance: Notices of the AMS, vol. 43, no. 12, > > December 1996: > > <http://www.ams.org/notices/199612/index.html> > > > The 9th Fermat number F_9 = 2^(512)+1 had been factored > > around 1990 by the Lenstras et al using the Number Field > > sieve (which had supplanted the quadratic sieve). > > > The Quadratic sieve is easier to understand than the > > Number Field Sieve, which I don't understand. > > > F_10 and F_11 were fully factored then, using the elliptic > > curve method (which can find smallish prime factors). > > > F_12 was listed as not completely factored, with > > F_12 being a product of 5 distinct odd primes and > > the 1187-digit composite: > > > C_1187 = > > 22964766349327374158394934836882729742175302138572\ > > [...] > > > 66912966168394403107609922082657201649660373439896\ > > 3042158832323677881589363722322001921. > > > At 3942 bits for C_1187 above, what's the > > probability density function of expected time > > till C_1187 is fully factored? > > For the Fermat number F_12 = 2^(2^12) + 1 or > 2^4096 +1 , another prime factor was found around > 2010. So, this new prime factor would be a divisor > of C_1187, a 1187-digit number. F_12 is listed > as known to be "not completely factored". > > The relevant line on the Web-page referenced below contains > the text: "M. Vang, Zimmermann & Kruppa" in the "Discoverer" > column: > <http://www.prothsearch.net/fermat.html#Complete> > > Also, lower down in the page, > "50 digit k = 17353230210429594579133099699123162989482444520899" > > This does relate to a factor of F_12 by PARI/gp. > Then, by my calcultions, the residual unfactored part > of F_12 has 1133 decimal digits and is a composite number. > > > Or, centiles: e.g. 50% chance fully factored > > within <= 10 years. 95% chance fully factored within > > <= 95 years, etc. ... > > Maybe 50% to 50% chances for "fully factored by 2100 " ? > (or 2060, or 2200 etc. ... ) > > dave
Is reading out a binary tree from smallest to biggest in anyway related to TSP, i have slight memory of doing a algoritmic solution for TSP when i tried to factor RSA primeproducts, unfortunatly it is all gone from my mind. Could you please make a short layman approach for how TSP and sorting is related to factorization it may come back to my memory. I lack the key so to speech to the problem.