The Prime Number Theorem, an introduction ← Number Theory

[@CodeSolidJohn]

I think some others mentioned this, but you mention x/log(x) and 1/log(x) without specifying that log in this case is log_e, or in other words, ln, the natural log of n. Of course, one can look that up, but it would be nicer if the video had it.

[@PunmasterSTP]

I think this video was a good prime-r, and I'd love to see more!

[@EnthuGamerush]

This was *so helpful,* thank you so so much!

[@ffhashimi]

I think this video is too brief to give a any good idea about Prime number theorem and it's crucial importance in number theory , Math and to the whole of science . you didn't mentioned why Prime number are important? the irregular distribution of Primes in number line ? the answer which given by Prime number theorem to the distribution of the Primes , and the limit of this answer . I like Socratica videos and they are very useful, but this one I am not sure about it . any way thank you for the effort .

[@Socratica]

Thanks for your feedback! To be honest, we totally agree with you. :) When we first started making videos, we were focused on making them short. Today, however, we take as long as necessary to fully explain a topic. Someday soon we'll make another video on the Prime Number Theorem. A proper treatment will likely take 10-15 minutes.

[@ffhashimi]

I am happy to get this positive reply; I agree with your recent approach which is topic based rather than time based ; you are doing a great job .. very useful and very important .. keep it !

[@paula19335]

@@Socratica do it please

[@MikeChaseJr]

If you redo it eventually, can you keep the scale on the pi(n) function the same on the x and y plane? The scaling you uses made it seem like every number was prime and I would’ve saw the relationship better if it was square, unscaled.

[@ariellalee4749]

Great video, thank you! Your videos are very pretty!

[@crystabelle5658]

im still confused.

[@jonahansen]

Isn't there an error at 1:28 where the first n integers will have 1/ln(n) primes? Shouldn't it be n/ln(n)? What am I missing?

[@zenicv]

i was wondering the same. It looked like an error. But they are talking about **Prime density** in which case it is correct. If we are talking about the actual number of primes, it is like you wrote.

[@premium.opinions1234]

I noticed that mistake as well. n/ln (n) might be the right formula.

[@EpicFrogzacula]

It's the natural log not the common log right?

[@renatofernandes1086]

yes, it is.

[@GarryBurgess]

Natural log is log to base e, whereas the common log is log to base 10. They are not at all the same.

[@Nombrespremiers-info]

The prime numbers distribution is here: accueil | loqiquedespremiers

[@_catzee]

you should've put x(n) at 0:45

[@thearindamroy]

Thanks you

[@ekeebobs7520]

Although I absolutely adore your videos, this however is too short.

[@pawanyadav3399]

Nice

[@Mw2Legend99]

I need the song :( Can someone help me?

[@RodrigoLimaStealth]

kzbin.info/www/bejne/jIDLo2x6fZV_aa8

[@dalilarobledodebasabe191]

Music by ...?

[@RodrigoLimaStealth]

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[@sovanbasu270]

Nice

[@gekuhgeng4912]

Tq

[@ryanenzokana3584]

still confused

[@prasunkumar182]

It is not pi it is phi

[@sharonjuniorchess]

Its just a function label that calculates an approximate number of prime numbers contained up to a number n: n/log n (where log is the natural log). It could be given any label it would not change the result.