Thread for posting tiny primes

[science_man_88]

Originally Posted by science_man_88

http://upload.wikimedia.org/math/5/5...95030ecf64.png

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

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

[3.14159]

Easy. That is exp(1). Also; 2.718281828459045..

[science_man_88]

thanks pi

[science_man_88]

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

[CRGreathouse]

Originally Posted by science_man_88

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

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

[3.14159]

Progress:

22:32:00 35667 k's remaining. p=36863449641229 divides k=1218543

[science_man_88]

Originally Posted by CRGreathouse

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.

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.

[science_man_88]

N=random(675);if(N>.5*450,print(N))

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.

[science_man_88]

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

[CRGreathouse]

Originally Posted by science_man_88

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.

"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.

[CRGreathouse]

Originally Posted by science_man_88

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

http://en.wikipedia.org/wiki/Prime_number_theorem