4937775 - Numberphile

4937775 is a Smith Number - as are 27, 666 and infinite others!
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran

[christopherpellerito]

For those saying that the huge number at the end is fake - it's for realsies. That huge number is over 10 million digits long but it isn't all that hard to prove that the sum of the digits in its prime factors equals the sum of the digits in the number itself equals 27, 400, 887. The number is cleverly constructed to produce that result.

Prime factors is the easy part. 10^1031-1 is obviously not prime because it contains nothing but nines and is thus a multiple of nine. But a string of 1031 ones IS prime, so the prime factors of that term are and the sum of the digits = 1037. The big number in the middle, 1000...0003000...0001 (4595 digit palindrome) is one of the longest known palindromic primes and the sum of its digits is just 5. Obviously 10^3913210 factors into 2^3913210 * 5^3913210.

So we know the sum of the digits in the prime factors already: 3 + 3 + 1031 + 5*1476 + 2*3913210 + 5*3913210 = 27, 400, 887.

It's a bit more work to prove that the sum of the digits in the number is the same, but basically what you end up with is a number that contains 2953 "clumps" of digits separated by long strings of zeroes, and each clump's digits add up to 9279. 2953*9279 = 27, 400, 887.

[akkalat]

Whoever calculated the largest Smith number must be a god among men.

[sphinx]

*I feel like this guy is the nicest guy you'll ever

[innocent_fugitive]

"42!" "Yay…". I love Professor Copeland's reaction. He's so awesome.

[Luxatos]

One thing not mentioned in this video is that Smith numbers are, by definition, composite numbers.  That's why 1, 2, 3, 5 and 7 aren't considered Smith numbers.

[LakeNipissing]

I could listen to Professor Ed all day, such a calm voice.

[Envergure]

If it weren't for this video, I would never have known that my grandmother's phone number has an eight-digit prime factor. Thank you from the bottom of my heart :)

[sethamajig]

My phone number is ALMOST a smith number:

Prime sum: 32
Digit sum: 33

Dang it

[GeneralAceTheAwesome]

So the answer to the first Smith Number is the answer to the ultimate question of life, the universe, and everything?

[NyanSten]

The number is from NANP (United States), calling it won't work in the UK. With some more information about the origin of the number, it's quite easy to guess the area code but it is no longer listed as belonging to a Smith in the phone book (the whole area was renumbered in 1990s). Please don't call that person.

[SpaghettiRoad]

I love how hapiliy Brady exclaims 42 when he hears the sum :D
I have a quick question though, Why are the one digit primes (2, 3, 5 and 7) not considered smith numbers? They might be trivial, when they themselves are their own sum of the digits, and primefactorization, but they still follow the definition? :)

[CatnamedMittens]

He must've been super nervous the way he was shaking.

[DexBunny]

My phone number turned out to be a smith number and I am amazed!

[numberphile]

Add its digits and add its prime factors using the method described.

[Grozdor]

5:04 just when I thought I would be the person who discovered the largest Smith's number using my phone number...

[OG_CK]

The smallest smith number is 2
prime factors=2
digits=2

[OMGGsummerxoxo]

Just a heads up. The closed captioning has Ed Copeland's name as James Grimes. However helpful that is now. ;)

[KasabianFan]

Why do subtitles say his name is James Grime?

[EdPwnz]

Largest known Smith Number is immense... thought it was going to be a much smaller number when he was about to mention it. Props to the peeps who discovered it, and props in advance for those who discover an even larger one.

[Schenkel]

I've calculated the last number that was prsented on this video, just so that the morbidly curious would satiate their lust for useless knowledge. This is what came up:
Error