I love primes....
What is the percentage(approx.) of positive integers less than a googol which are primes?
Details
Round your answer to one decimal place
The answer is 0.4.
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1 solution
Classic! Nice approach :D
@Kartik Sharma - What resources do you use to learn Number theory? Please be specific. Don't just say internet or something like that.
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No, really my answer still would honor internet once again. But yeah, to be specific, YouTube has been of great great help and yeah Wikipedia, even. Yahoo answers must also be included. And yes, as a friend, I will also tell you to check out OEIS and AoPS, also. Coming to the books, Number theory chapter of Brain Mapping Academy Mathematics Class 9 is good.
P.S. - But don't you think a level-3 (actually level 4 but deserving level 3) should suggest something to a level 5 born genius. And so, you must also tell me your resources and yes, be specific. ;)
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hey, why don't you check my new problems and yeah if you like, re-share them(advertising;)
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@Kartik Sharma – Sure. I would. But I cant solve any of them :P. How do you do infinite series without calculus? Or do you know calculus? Well, I would say that despite me being a level 5, there are some topics in which you are better than me. So I wouldn't say number theory is my forte , but I definitely think its one of my favourite topics since childhood. I'm gonna miss doing all this on Brilliant after school reopens. :( Whatsay? When does school reopen? Will you continue to do this even after that? @Kartik Sharma
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@Krishna Ar – I have started learning calculus from Khan Academy... But yeah, I am not at all good in it......
Yes, I must agree that school sometimes(or I mean every time ;) ) become boring and yes as you say "throttle" in some way our studies..... And yeah, Brilliant which has established a crucial part in my heart in these holidays, will definitely be missed. My school would reopen on 7 July and I think that your school will also be opening the same day. I will try to continue with my same routine(although I have to change) and yeah, will give at least 1 or 1/2 an hour to Brilliant.
P.S. - I will also miss(or enjoy being ended) the anxiety of completing my summer holiday homework......... Oh sorry, what's that??? ;);-););-)
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@Kartik Sharma – 7 july? Mine opens tomorrow :(
@Kartik Sharma – You are so lucky to have so long hols. :( I totally suck. When did vacs start for you
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@Krishna Ar – My school closed on 17 May. Yours must be some days before...
@Kartik Sharma – Hey, resources- I actually am yet to get a proper resource, but even If I get one, I'm sure school won't allow me to use it. (I mean school will throttle the life out of me). I have a few books which contain a lot of problems (tough) on general number theory. And Bma is quite tough!!!!!!. And I deserve only a level 4 in number theory...maybe early level 5 ... :-/
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@Krishna Ar – Few books which contain a lot of problems(tough)?????
Can you please mention all the books you read and which helped you to achieve a level 5 in NT ??
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@Kartik Sharma – As I already told you, I don't deserve a level 5. People better than me are still at level 4.
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@Krishna Ar – books, mention them!?!?!?!
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@Kartik Sharma – I dont really study from any book. IF u asked about the problem collection- They are called GEMS.
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@Krishna Ar – GEMS? That must be a joke as far as I am getting it..
By the way, level 5 is still not an easy think. Please tell me some 'specific' resources you use?
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@Kartik Sharma – GEMS ain't a joke. That's what fetched me national glory. I wish it does this year too. I can prove to my peers that coaching is not necessary
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@Krishna Ar – I don't know anything about GEMS.... What's it?/
@Kartik Sharma – Dude, please tell me how do you do infinite series
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@Krishna Ar – I don't know..... I really don't know.....
Okay, can I as you a question? - What do you think is your strongest point in Number Theory and why do you want to become a Doctor(if I am not wrong)?
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@Kartik Sharma – I dont know dude, I really dont know -_-. You'd better tell me how.
I actually hate videos! :( Is numberphiles good? U said u had used it?
I actually almost gave up because my initial answer "0.436" which was marked wrong... @Karthik could you add "rounded to one decimal place" in your question.
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Oh sure, sir, I will and sorry, by the way
I've updated past answers to allow for those close to 0.435.
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But it still marked my 0.434 as incorrect. So sad
From PNT,
we know that no. of primes ∼ n/ln(n)
Therefore, pi(n)/n ≈ 1/ln(n)
Hence, pi(googol)/googol ≈ 1/ln(googol)
Googol = 10^100
Therefore, proportion of primes ≈ 1/(100 ln(10))
≈ 1/230.25
≈ 0.004.....
So, perecentage ≈ 0.4 %