[QUOTE=science_man_88;230818][url]http://upload.wikimedia.org/math/5/5/9/55978f02e2b22e9a93943595030ecf64.png[/url]

if this is what you mean with n replacing k I'll see what I can do.[/QUOTE]

I can't remember what Pari uses for 2.71818 etc.

Easy. That is exp(1). Also; [B]2.718281828459045..[/B]

thanks pi

poisson(n,lambda) = (lambda^n*exp(-lambda))/n! best I could understand the first.

[QUOTE=science_man_88;230825]poisson(n,lambda) = (lambda^n*exp(-lambda))/n! best I could understand the first.[/QUOTE]

Good. Can you do the second? It's almost exactly like the first.

Progress:

[code]22:32:00 35667 k's remaining. p=36863449641229 divides k=1218543[/code]

[QUOTE=CRGreathouse;230810]As a first step, can you write a program that takes lambda and n, and returns the probability that exactly n Poisson events occur when lambda are expected to occur?

As a second, can you write a program that takes N, t, and n and returns the probability that out of t random numbers near N, exactly n are prime? Treat this as a Poisson process where each number has probability 1/log(N) to be prime.[/QUOTE]


well I gather that n is k and t is lambda if placed in the equation so the hard part on the second I think is making sure all t numbers generated are "near" without knowing what near is defined as. I found Pari's number generator and I can plug in something like 1.5*N as covering a sufficient range but that may be too large.

[CODE]N=random(675);if(N>.5*450,print(N))[/CODE]

this works to bound it greater than .5 the original value: so I think I'm nearly there just got to put it all together in a way to make sense.

I'm looking at this wrong lol as i don't know the formula for near a given N I'll double check though.

[QUOTE=science_man_88;230865]well I gather that n is k and t is lambda if placed in the equation so the hard part on the second I think is making sure all t numbers generated are "near" without knowing what near is defined as. I found Pari's number generator and I can plug in something like 1.5*N as covering a sufficient range but that may be too large.[/QUOTE]

"Near N" means that the probability that each is prime is 1/log N. You expect a total of t/log(N) primes. Now apply the Poisson distribution.

[QUOTE=science_man_88;230870]I'm looking at this wrong lol as i don't know the formula for near a given N I'll double check though.[/QUOTE]

[url]http://en.wikipedia.org/wiki/Prime_number_theorem[/url]