Twin Proofs for Twin Primes - Numberphile

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NUMBERPHILE

Videos by Brady Haran

[jdmarino]

Ben Sparks must be a great math teacher. Energy, big smile, almost childlike wonder.

[Wool_Scarf]

The mod9 being equivalent to digital root is insane to me, despite being such a simple proof

[rudranil-c]

I like Ben Sparks the best among all the brilliant mathematicians who appear on this channel. I still cannot forget the chaos theory video and the one with the mandelbrot set from Ben. Thank you.

[ericvaninwegen]

The algebraic proof also shows why 3, 5 doesn't fit the pattern. Since (n-1) = 3 in this pair, the conjecture that n = 3k is wrong. Neat!

[RiseUpUNAFRAID]

I miss my twin brother, he passed several years ago 😢. I'll see him soon.

[anttheknee]

You can use the same proof to prove that all cousin primes (4 apart) will have a digital root of 5, and sexy primes (6 apart) greater than 7 will have a digital root of 4

[karlwaugh]

The second proof showed that although "Brady's Conjecture" was false, it has a cousin - that the digital root of the product of two integers either side of a 3 is 8 - was true. I think that although the second proof is neater, it does also highlight that it's not *really* to do with them being twin primes but rather them hugging multiples of 3.

[tristanc]

12:06 "We proved by thinking..." Is such a great line!

[RAG]

Twin primes are of the form 6n-1, 6n+1. Multiply then gives 36n^2-1. Digit sum of 36 is 0. 0 times n^2 digit sum is 0, so digit sum of 36n^2 -1 is -1, which is 8

[edgarleft]

You can make this even more impressive. The product of two twin primes is also actually one less than a multiple of 36. You can proof this by doing the second proof and realizing that twin primes are always 1 mod 6 and 5 mod 6, which I believe was a numberphile video as well.

[VietVuHunzter]

This bring back so much memory to me. Modulo arithmetic was fascinating to me when I was in middle school.

[NunoSalvaterra]

In Portuguese, the digital root operation is informally called "noves fora" which means "nines out". 😀

[trollme.trollmehard.]

You know...I think I need to learn how to write proofs and videos like this are going to help get me there. Thanks.

[martinepstein]

Great video. Ben is slightly mistaken at 13:05. As he showed, the product is 9k^2-1. To get +8 you have to rewrite it as 9(k^2- 1)+8

[ssir-to]

"Proof by thinking" 12:04 my new favourite method

[brianvanhoff]

I noticed that the digital root of the product primes with a difference of four seems to come out to 5 each time.

[hyfy-trjy]

I see our resident "Maximus Mathmaticus" is back...and yes we are entertained!

[gcewing]

So to reduce a number mod m, all you have to do is convert it to base m+1, find the digital root, and convert back!

[RudyHHOfficial]

There's another infinite sequence of twining:
Step 1: Take a prime pair.
Step 2: Multiply those.
Step 3: Subtract that until you reach a twin prime.
for (3, 5), I did:
_(3, 5)_
(11, _13_ )
(137, _139_ )
and
( _18_, _919_, 19, 079)

[themaskedcrusader]

Thanks to the second proof, we know that the product of twin primes will always be one less than the square of the number in between. that's kinda cool