Thread for posting tiny primes - Page 58

CRGreathouse · 2010-09-22, 23:35

Quote:

Originally Posted by 3.14159

Is the above the code for Charles's (grammatical error?) request?

#619? I think that was sm's attempt, but it's not correct.

I spell the genitive Charles' but you can spell it as you prefer.

3.14159 · 2010-09-22, 23:37

I think I might have already been answered here.. But is there any function which gives the percentage of whole numbers that have no prime divisors ≤ n?

If I've already been answered, link me to the post which answers this.

Is it (p(n)/(euler's totient(p(n)))? Where p(n) represents the nth primorial number.

CRGreathouse · 2010-09-22, 23:39

Quote:

Originally Posted by 3.14159

I think I might have already been answered here.. But is there any function which gives the percentage of whole numbers that have no prime divisors ≤ n?

If I've already been answered, link me to the post which answers this.

http://mersenneforum.org/showthread.php?t=12022

science_man_88 · 2010-09-23, 00:15

Quote:

Originally Posted by CRGreathouse

Maybe you can ask sm that question once he finishes the script!

32

sorry I don't know a formula with N,t,L and p for n

science_man_88 · 2010-09-23, 00:49

Code:

 estimatePrimes(N,t,n,L)=my(lambda=(t/log(N))*(exp(Euler)*log(L)));(lambda^n*exp(-lambda))/n!;

god I'm an idiot !

so how to manipulate for a formula for n

with N,t,l and p I can get as far as plugging them into this. but I don't know how to get n from it.

science_man_88 · 2010-09-23, 01:01

reducing it to basic variables

Code:

p = ((t/log(N))*(exp(Euler)*log(L))^n*exp(-((t/log(N))*(exp(Euler)*log(L)))))/n!;

CRGreathouse · 2010-09-23, 01:02

Quote:

Originally Posted by science_man_88

so how to manipulate for a formula for n

with N,t,l and p I can get as far as plugging them into this. but I don't know how to get n from it.

You're solving, I think, for t if we use the variables in your code.

Post the formulas and let's see how far you can get in solving it. I'll post half of the unsolved equation (the other half is the definition of lambda):

$p=\frac{\lambda^0e^{-\lambda}}{0!}=0.01$

This is the special case I asked about: n = 0 (finding 0 primes with probability 1%).

science_man_88 · 2010-09-23, 01:11

Quote:

Originally Posted by CRGreathouse

You're solving, I think, for t if we use the variables in your code.

Post the formulas and let's see how far you can get in solving it. I'll post half of the unsolved equation (the other half is the definition of lambda):

$p=\frac{\lambda^0e^{-\lambda}}{0!}=0.01$

This is the special case I asked about: n = 0 (finding 0 primes with probability 1%).

funny I took lambda and replaced it in the equation with what it's value was told to be in other variables.

science_man_88 · 2010-09-23, 01:28

with the original form i can get as far as:

Code:

p/exp(-lambda)=lambda^n/n!

but that's obvious

why I said trouble with log is it can go to

Code:

log(p*n!/exp(-lambda))/log(lambda)=n

but then there's a n term in the log to get out of it.

CRGreathouse · 2010-09-23, 01:58

Quote:

Originally Posted by science_man_88

but then there's a n term in the log to get out of it.

No, there isn't. n is a constant equal to 0, and p is a constant equal to 0.01.

science_man_88 · 2010-09-23, 11:21

Quote:

Originally Posted by CRGreathouse

No, there isn't. n is a constant equal to 0, and p is a constant equal to 0.01.

in your special case n is defined if i want to make a script it isn't.

in your special case p = $e^{-lambda}\over 0$

2010-09-22, 23:37	#629
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	I think I might have already been answered here.. But is there any function which gives the percentage of whole numbers that have no prime divisors ≤ n? If I've already been answered, link me to the post which answers this. Is it (p(n)/(euler's totient(p(n)))? Where p(n) represents the nth primorial number. Last fiddled with by 3.14159 on 2010-09-22 at 23:40

2010-09-23, 00:49	#632
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	Code: estimatePrimes(N,t,n,L)=my(lambda=(t/log(N))(exp(Euler)log(L)));(lambda^n*exp(-lambda))/n!; god I'm an idiot ! so how to manipulate for a formula for n with N,t,l and p I can get as far as plugging them into this. but I don't know how to get n from it.

2010-09-23, 01:01	#633
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	reducing it to basic variables Code: p = ((t/log(N))(exp(Euler)log(L))^nexp(-((t/log(N))(exp(Euler)*log(L)))))/n!;

2010-09-23, 01:28	#636
science_man_88 "Forget I exist" Jul 2009 Dumbassville 10000011000000₂ Posts	with the original form i can get as far as: Code: p/exp(-lambda)=lambda^n/n! but that's obvious why I said trouble with log is it can go to Code: log(pn!/exp(-lambda))/log(lambda)=n but then there's a n term in the log to get out of it. Last fiddled with by science_man_88 on 2010-09-23 at 01:36*

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