- I'm going bonkers here, I can't get rid of a factor of 2 'error'.

I'll start with the assumtion that the probability of a number P being prime is ln(P).

Numbers of the form k.233#-1 cannot have primes 2..233 as factor

Therefore the density of primes is increased by

(2/1) * (3/2) * ... * (233/232)

= 9.84256

However, I've run some tests, density of primes seems to have increased by a factor of about 5.5.

I notice that ln(233) is 5.4

Should the density increase by 5.4 or 9.8?

Phil

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Support Eric Weisstein, see http://mathworld.wolfram.com

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http://www.shopping.altavista.com - Phil,

"Probability" is not the correct word here.

Probabilities are no greater than 1.0, like the

probability of getting "snake-eyes" in dice is 1/36.

And, ln(100) ~ 250 >> 1.0

Perhaps, you mean something else like

the GAP between two primes is approximately, ln(n).

Milton L. Brown

miltbrown@...

PS - Are the above two "primenumber" addresses the same?

Phil Carmody wrote:

> I'm going bonkers here, I can't get rid of a factor of 2 'error'.

>

> I'll start with the assumtion that the probability of a number P being prime is ln(P).

>

> Numbers of the form k.233#-1 cannot have primes 2..233 as factor

> Therefore the density of primes is increased by

> (2/1) * (3/2) * ... * (233/232)

> = 9.84256

>

> However, I've run some tests, density of primes seems to have increased by a factor of about 5.5.

> I notice that ln(233) is 5.4

>

> Should the density increase by 5.4 or 9.8?

>

> Phil

>

> Mathematics should not have to involve martyrdom;

> Support Eric Weisstein, see http://mathworld.wolfram.com

> Find the best deals on the web at AltaVista Shopping!

> http://www.shopping.altavista.com

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

> The Prime Pages : http://www.primepages.org > Numbers of the form k.233#-1 cannot have primes 2..233 as factor

Fine. By Merten's Theorem, this is approximated by ln(233)/0.56 = 9.73.

> Therefore the density of primes is increased by

> (2/1) * (3/2) * ... * (233/232)

> = 9.84256

> However, I've run some tests, density of primes seems to have

Two thoughts occur to me - either you may be being lucky here (these things

> increased by a factor of about 5.5.

> I notice that ln(233) is 5.4

are fairly random, after all), or you may be measuring things wrongly (don't

forget that the ln(P) probability includes the even numbers as well).

> Should the density increase by 5.4 or 9.8?

I would say 9.8.

Paul.

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