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RE Prime f(p,x,y)

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  • Jose Ramón Brox
    You have X*Y possible cases, where X is the range for the x and Y the range for the y. Let s call T to the favorable cases (number of primes discovered within
    Message 1 of 1 , Sep 1, 2003
      You have X*Y possible cases, where X is the range for the x and Y the range for the y. Let's call T to the favorable cases (number of primes discovered within these ranges). The probability of a number P of your formula being prime is moreless q= T / X*Y. If multiplying the range of one of them you roughly increase the T in the same order, then q is near constant, Y ' = 2Y , T' = 2T --> q' = q.

      Then, supposing that this statement is true for every range of X and Y, we already now that q=83 / 10*70 = 0,119 = 11,9% of primes (for the other data, it goes down to 11,5%).

      To me it seems not to be very big. And experience tells me that the probability may decrease when p,x,y increases (without seeing the formula! ;-P).

      Regards. Jose.
      ----- Original Message -----
      From: Mark Underwood
      To: primenumbers@yahoogroups.com
      Sent: Monday, September 01, 2003 9:44 PM
      Subject: [PrimeNumbers] Re: Prime



      That's OK Navid, many of us have been there! We get so focused and
      narrowed in on something that we loose sight of the obvious.

      Now that I'm typing, I must say that I just love that little picture
      at the Home page of this Yahoo Prime group! It shows two little
      people standing before an awesomely big statue of the number '2'.

      Now, about generating primes. I'm currently investigating a very
      simple function, call it P(p,x,y), which is very good at generating
      primes of all kinds. In fact on cursory examination it seems that if
      one, say, doubles the range of x covered, the number of primes
      produced almost doubles. If one doubles the range of y covered, the
      number of primes produced almost doubles as well. For example for one
      particular (and typical) p, if x ranges from 1 to 10 and y ranges
      from 1 to 70, 83 primes are produced by the function. If the range of
      y is allowed to double, that is from 1 to 140, 161 primes are
      generated. In the first case when y ranges from 1 to 70, the lowest
      prime produced is 379 and the highest is 15196639291. Most of the
      numbers are over 7 digits.

      Is this ordinary, good, or too good to be true?


      Mark



      --- In primenumbers@yahoogroups.com, "navid_altaf" <navid.altaf@g...>
      wrote:
      >
      > Oh dear. Its finally dawned on me I'm just stating the obvious
      > by definition. Sorry. I'm going to try to stop thinking about
      > prime nos for some time (I can almost hear your collective sigh of
      > relief).


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