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312 results from messages in primenumbers

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  • Hi jp! I don't know if I am understanding you well. The only natural numbers that cannot be written as a difference of two squares are those of the form 4n+2, i.e., the numbers which are even but not divisible by 4; the rest of them are all differences of two squares. In particular, if n=2k+1 is an odd number, then (k+1)^2-k^2 = 2k+1 = n. Therefore R19 IS a difference of two...
    Jose Ramón Brox May 29, 2014
  • Dear sinclair75: In ill-conditioned systems and chaotic systems , precision is paramount (because a little error in the input data produces a huge error in the output data or in the extrapolation to future steps, respectively). I think a good example is weather forecasting. Nevertheless, approaches to avoid this undesirable situation do exist: for example, an infinite-digits...
    Jose Ramón Brox Mar 8, 2014
  • 2013/7/26 djbroadhurst > ** > > > > > --- In primenumbers@^$1, > Jose Ram�n Brox wrote: > > > Now that I think about it better, > > I see that I was fooled by your proposal! > > Indeed you were :-) > > Yeah, you are so right! Hehe You can see that I don't know that much Pari-GP programming; I thought that "polinterpolate" of the vector V was interpolation at (V, [0 ... 0]), but...
    Jose Ramón Brox Jul 27, 2013
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  • 2013/7/27 Jose Ram�n Brox > > (But if you paste David's program on Pari and correct the missing }, you > will get a glimpse of it, if so you wish). > > What I really wanted to say is: if you paste David's _polynomial_ and add the _necessary_ }, you will get it. You must also erase the ";", like this: {Poly=polinterpolate(vector(100,k,prime(137*k-104)))} > Jose > > > >> Werner...
    Jose Ramón Brox Jul 27, 2013
  • 2013/7/26 Alexander > ** > > > > > I don't have your math program. > That's Pari-GP, Alexander. You can get it here: http://pari.math.u-bordeaux.fr/ (It seems not to be working right now). Can I get your P(n) explicitly? > Do you really want us to paste here a polynomial of degree 99 with big rational coefficients? To see what I'm saying, its independent term is...
    Jose Ramón Brox Jul 27, 2013
  • Now that I think about it better, I see that I was fooled by your proposal! :D What we want is not a polynomial whose _roots_ are primes, what we want is a polynomial which generates as much primes as possible with its _image_. I.e., what we want is to maximize p such that the sequence p({1,2,3,...}) gives the biggest possible "prime head". The classical example of Euler, p(x)=x^2...
    Jose Ramón Brox Jul 26, 2013
  • 2013/7/26 djbroadhurst > ** > This polynomial performs better: > > polinterpolate(vector(100,k,prime(k))) > > Sure! But it (I suppose) does not satisfy the implicit assumption (explicit in the contest) that the primes must be consecutive. Regards, Jose [Non-text portions of this message have been removed]
    Jose Ramón Brox Jul 26, 2013
  • A few years ago there was a programming contest from Al Zimmermann looking for the best prime-generating polynomials. The best results are essentially found in this page: http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html The best one is [image: 1/4(n^5-133n^4+6729n^3-158379n^2+1720294n-6823316)]. Regards, Jose Brox 2013/7/25 Chroma > ** > > > Alexander wrote: > > > > Let...
    Jose Ramón Brox Jul 25, 2013
  • 2013/6/25 John > (6) Is there any authority who has attempted to make some kind of popular > assessment of the problem, Zhang's approach, and the subsequent work? > This one I can answer: http://terrytao.wordpress.com/2013/06/04/online-reading-seminar-for-zhangs-bounded-gaps-between-primes/ I'm also interested on the answers to your other questions, although it is obvious that that...
    Jose Ramón Brox Jun 25, 2013
  • Thank you both for the info! Jose 2013/6/7 djbroadhurst > ** > > > > > --- In primenumbers@^$1, Jose Ram�n Brox > wrote: > > What if we ask for 3^n�k+1 or more generally, for a "base" b^n�k+1? > > http://www.mersenneforum.org/showthread.php?t=9738 > > David > > > -- La verdad (blog de raciocinio pol�tico e informaci�n social) [Non-text portions of this message have been...
    Jose Ramón Brox Jun 7, 2013