## RE Prime f(p,x,y)

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• 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
Sent: Monday, September 01, 2003 9:44 PM

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

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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