Primes are like Weeds (PNT) - Numberphile

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NUMBERPHILE

Videos by Brady Haran

[pamanes]

you should do a video where he explains his Phd thesis to us mortals

[ChrisBandyJazz]

How about you just change your name to James Prime?

[tubrutolity]

Read the title and was like "Smoke primes everyday"

[snelo]

The constant e can be remembered by using the following: Andrew Jackson was president of the USA in 1828; and the angles of an isosceles right angled triangle are 45, 90, 45.
So remember 2.7; Andrew Jackson; Andrew Jackson; isosceles right angled triangle
That is: 2.7 1828 1828 459045 which is e to 16 decimal places

[NFSHeld]

I just realized the insane amount of abstraction Maths has. At 6:25 he literally said "If you pick any number, let's pick n, ...". Usually, everybody would say "Erm... 'n' of all things you could've picked is not a number, it's a letter." But in Maths, everybody is fine with it. Imagine there was some weird field of science where you'd say "Pick any vowel, let's pick 'k', ..." and everybody silently nods and goes on to listen the rest of the sentence. It's so weird in a sense.

[pfl]

I actually find this site more interesting than 12 years of elementary to highschool education....

the comments are great too. People discussing about this and that. Makes young audiences interested in maths. I hope teachers use this channel

[PopeLando]

I recently found this useful when discussing cryptography. RSA cryptography (simple) creates an asymmetric cypher by providing a very large unfactorisable number (ie the product of two enormous prime numbers) with which you perform a modular exponentiation. Currently a lot of implementations use 1024-bit prime numbers to build the cypher number. So if you were trying to find prime numbers represented by 1024 bits, how many prime numbers is that? Well, base-2 log of 2^1024 is 1024. e is between 2 and 3 (closer to 3) so the natural log of a number is likely to be approximately 2/3 of the base-2 log. But in any case, base-2 log of 2^1024 being 1024, we know that "pi" is going to be no smaller than 1/1000 of 2^1024. Well, if you have a calculator that can handle large exponents (eg MS Calc for Win10 can) you'll find that 2^1024 is about 1.8x10^308. ln(2^1024) is about 710, and so pi(2^1024) is 1.8x10^308 / 710, which is 2.5x10^305. So the PNT tells us that in the realm of 1024-bit numbers, ie 10^308, the number of primes is 10^(308-3) or a still massive 10^305.

[Magickmaster]

It is funny that when i started watching numberphile, i didnt understand anything and now i understand EVERYTHING they say!

[IntimateMuffin]

If anyone is interested by this video, I highly recommend the book "Prime Obsession" by John Derbyshire. I read through this book as a senior in high-school, and even though I did not fully comprehend the proofs of the theorems presented, it was a great read and really enhanced my problem solving methodology. The author elaborates on Bernhard Riemann and his Hypothesis, and the Hypothesis' intimacy with the PNT. Every other chapter also includes history of the PNT and it's contributors.

[yash]

4:03 i like twin primes
example for reminding myself: (5, 7); (11, 13) and so one.

[WalrusRiderEntertainment]

Wow I actually could follow that . Yay..

[TuhinDas]

Why dont u do videos with JAMES GRIME anymore Brady? 
His videos are great.. So simple explanations

[TitleistGuy]

I love mathematicians.

As an engineer I always thought I had a handle on math but honestly thats barely scratching the surface and these guys and gals on this channel are the people that really get math.

[Coffeeismylifeblood]

I’m smiling from ear to ear because I’m in the edge of my seat

[DanielEyassu]

These videos just blow my mind every time. Thanks Brady and Dr.Grime

[kapitan_black_pearl]

this title is so right, every time I see prime numbers i get so high. there is no multiple to explain this euphoric feeling

[MadNotAngry]

Only understand about half of all your vids, Numberphile... but enjoy each and everyone.

[PhilBagels]

That means there is at least one prime between Graham's number and 2x Graham's number. So all you have to do is search that limited interval, and you'll find the biggest prime so far! So get to work!

[naveenchandrakumar]

Most important thing I like in you is the amount of enthusiasm you have to know about the properties of these numbers. Great explanation of the PNT.

[elibaum]

When I first saw the title, I thought it said, "Primes are like Weed"... lol