A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
A positive integer is picked randomly from 10^(10^61) to 10^(10^70), inclusive.
What is the probability that it is prime?
anonymous
 4 years ago
A positive integer is picked randomly from 10^(10^61) to 10^(10^70), inclusive. What is the probability that it is prime?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but numerator is negative, denominator is positive?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i would not bet a stick of gum that the answer is right

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well that is wrong! yikes

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\pi(n)\approx \frac{n}{\log(n)}\] embarrassing too let me get rid of it

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0let me try the algebra again.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i can't write with all these powers to powers, so lets put \[m=10^{10^{60}}\] \[n=10^{10^{70}}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then i guess you estimate at \[\pi(n)\pi(m)=\frac{m\log(n)n\log(m)}{mn}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so dividing by total number of numbers between them you get \[\frac{m\log(n)n\log(m)}{mn(nm)}\] but i have a feeling there is a much better and more sophisticated way to do this

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do you know the answer?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i'd say the answer is nearly identical to 1/ln(10^(10^70)) which is less than 1 in 10^70 chance of getting a prime

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0when comparing n and m, you might use the fact that n is much bigger than m. try n = 10^(69999999990000..[61 zeros]...0000) * m or something ... rewrite all the algebra so that m/n terms can be discarded when compared to non(m/n) terms

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0also it might be \[\pi(N)  \pi(M) \approx \frac{N}{\ln(N)}  \frac{M}{\ln(M)}\]and\[\frac{\pi(N)  \pi(M)}{NM}.\]I would show that second equation is \[\frac{1}{\ln N}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.