Why is this number everywhere?

- Let me show you something unbelievable. Name a random number between 1 and 100. - 61.

- Okay, that's pretty random. - [Emily] Just name a random number from 1 to 100, random. - 43.

- 43, thank you so much. - 56. - 7.

- I want the most random number between 1 and 100, like totally random. - 11. - 37.

- [Interviewee] 79. - 79, thank you so much. - 91.

- 7. - 3. - 37.

- [Derek] 37. - 37, yeah. - [Derek] Why 37?

- I dunno, it's the first number that came to my mind. - 44. - 27.

- 37. - 72. - 4.

- 13. - 7. - 37.

- [Emily] Really? (Derek speaking in foreign language) - 13. - 7.

- 37. - 37? - 73.

- 37. - 35. - 37.

- [Emily] 37, no way! - 43. - 2.

- 37. (Derek gasping) - I knew you were gonna do it. He just "37-ed" and walked away.

- Between 1 and 100. - Ah, no thanks. - [Emily] Okay.

- 37. - [Emily] Oh, perfect. Thank you so much.

- 83. - 37. - 37.

- 87. - 55. - 37.

- 37. (Emily gasping) Can I shake your hand? - [Derek] I love the thought you're putting into this.

- 37? - No, you are kidding me! Are you real?

- Yeah why? - Did we ask you this already? - No.

- Random number between 1 to 100. - 37. - 37.

Oh, my gosh, yes. - [Derek] Name a random number between 1 and 100. - 37.

- Are you kidding me? Why? - It's a good number, I guess, any number.

- [Derek] Where did that come from? - Imagination, I suppose. - So, what's going on?

Well, people are actually really bad at selecting things randomly. In fact, when asked to pick a color and a number, people reliably select blue and 7 the most across dozens of different cultures. Psychologists have a name for this pattern.

The blue-seven phenomenon. And when picking a random number between 1 and 100, it has long been suggested that the equivalent of the blue-seven phenomenon is the number 37. My producer, Emily, and I spoke to hundreds of people to test this theory.

The most common answer was 7, but maybe that's because people just expected that we'd ask them for numbers between 1 and 10. The most common two-digit number really was 37, much to our surprise. (Derek and Emily gasping) So we decided to embark on the biggest investigation ever on the number 37.

And it took us to some unexpected places. - I think 37 is a fascinating number. It's just really interesting because it turns up so much.

How many objects are there here in the room with us that have a 37 on them? I'm sure there's more than 1,000 here. I built the 37 Website in 1994.

I started getting email from strangers, it's everywhere. I'm trying to collect them all. We're tireless.

The tireless cabal of 37 people, yeah. - Apparently, people choose 37 so reliably that there's even a widespread professional magic trick that relies entirely on getting an audience member to just pick 37 out of thin air. It's called The 37 Force.

- I'm gonna ask you to think of a number in a moment, okay? It's a two-digit number, less than 50. Both numbers are odd, but different.

You could have 19, 17, or 15, but not 11. Because you see both numbers are the same, 1 and 1 next to one another. You ready?

One, two, and three. What number did you think of? - [Audience] 37.

- 37. Fascinating. In the famous Stanford MIT Jargon File, the origin of hacker slang, 37 is given as the random number of choice for computer programmers.

“When groups of people are polled to pick a random number between 1 and 100, the most commonly chosen number is 37. " (graphic buzzing) The thing is, no formal polls on this actually exist. The best we found was a Reddit poll of 1,380 people from four years ago, and the most popular number was.

. . 69.

But after that, the winning number was 37. But we can do better than a sample size of just 1,000 people. So we conducted the largest random number survey ever.

In a community post 3 weeks ago, we asked people to pick a random number between 1 and 100. We received 200,000 responses. Here are the results as they came in.

It's fascinating to watch how consistent these supposedly random numbers are, from 10,000, to 100,000, all the way up to 200,000 respondents. The distribution barely changes, suggesting that people from all around the world think about random numbers in a particular way, and it is decidedly not random. Ignoring the extremes of the scale because people were primed by the numbers 1 and 100 in the question itself, and ignoring 42 and 69 because they're not random, there are a few numbers that stand out, which we seem to regard as more random than the rest.

7, 73, 77, and 37. (pensive music) Then we asked people to pick the number they thought the fewest others would pick. The goal was to get rid of favorite or lucky numbers and give truly random selections.

And here, the results were even clearer. Again, ignoring the very extremes and 50 in the middle, the most selected numbers were, far and away, 73 and 37, which were nearly tied. The actual least-picked number in the first question was 90, followed by 30, 40, 70, 80, and 60.

Multiples of 10 apparently don't seem that random. The most picked overall numbers ignoring the outliers were 73 and 37. (pensive music) Ironically, all this evidence points to 37 and its inversion, 73, as not being random at all.

So why does everyone pick them? Well, one argument is that this is just how people perceive randomness. 37, does that feel random to you?

- Yeah. Yeah, it does. - [Derek] Yeah, 50 wouldn't be random?

- No. - [Derek] No. - It would be too contrived.

- [Derek] Yeah. - Yeah, it's too central - I think people think that even numbers are less random than odd numbers. - 5 feels not random, 9 and 1 feel too extreme, so people tend towards 3 and 7.

- This is backed up by the fact that every one of the top numbers in our survey consisted of 3s and 7s. In fact, 3 and 7 were the most selected digits on both questions. But there's also a mathematical case for humanity's number of choice because it's not just odd numbers, but specifically primes, which feel like the most random numbers.

Notice how we ignore odds ending in 5s or how something like 39 still feels a little less random than 37? Primes feel random for at least two reasons. First, they don't appear as much in our lives.

I mean, pixel counts, fruit boxes, square footage. We live in a composite world with multiple dimensions that multiply together, so we just don't see primes much past the single digits. Second, we don't have a formula for primes.

If you have a prime number and you want to find the next one, you have no choice but to check every number until you find a prime. The closest thing we have to a formula is the prime number theorem, which gives the approximation that the nth prime number occurs around n times natural log of n. For example, the 1,000th prime number should be around 6,908.

And it's close, but certainly not exact. So primes essentially occur at random, but of all the primes, 37 has reason to stand out. (pensive music) If we were to find the prime factors of every number, we would see that 2 is the smallest prime factor for exactly 1/2 of them, all of the even numbers.

And 3 is the smallest prime factor for 1/6 of all numbers, anything that's divisible by 3 but not by 2 and so on. As we pick larger and larger primes, they form the smallest prime factor for fewer and fewer integers. But, what if we track the second smallest prime factor of each number?

Well, first, we have 3, which is the second prime factor of a number. Only when the number is divisible by both 2 and 3 or divisible by 6. So 1/6 of all numbers have a second prime factor of 3.

And as we keep going, which number will end up at the balancing point? This is the median second prime factor of all numbers, all numbers from 1 all the way up to a googol and off to infinity. Would you believe that that number is 37?

(pensive music) Let's take a look at 5. 5 is the second prime factor only when a number is divisible by 5 and 3, but not 2. Or 5 and 2, but not 3.

In the first case, a number divisible by 5 and 3 means it's divisible by 15, so that's 1/15 of all numbers. But it also can't be divisible by 2. So 1/2 of 1/15 is 1/30 of all numbers.

In the second case, a number divisible by 5 and 2 means it's divisible by 10, but it cannot be divisible by 3. So we're left with 1/10 times 2/3 equals 1/15 of all numbers. Adding up these two cases, we get that 1/10 of all numbers have 5 as their second prime factor.

And we can repeat this for the next prime, 7. Just take each of these cases and add them up to get that 1/15 of all integers have a second prime factor of 7. And so on.

Keeping a running total, we quickly approach a balancing point for the second prime factor across all integers. And then we reach it. So the median second prime factor of all numbers is 37.

Half of numbers have a second prime factor of 37 or less. There are other remarkable qualities about 37 as a prime. It's an irregular prime, a Cuban prime, a lucky prime, a sexy prime, a permutable prime, a Padovan prime.

And at this point, mathematicians might just be making up types of primes. - 37's identity as a prime number is so strong that the same day I first learned the number 37, I learned it was prime. This was one of my first books as a toddler.

It teaches you every number from 1 to 100 with a short story or fun fact for each. So for 26, that's how many letters in the alphabet. Or for 30, they give the days of September.

Or for 52, that's how many cards are in a deck. Except 37. (pages rustling) (jaunty music) It's a prime number.

Nothing goes into it. Someday, you'll understand. I did not like that.

I understood every other number, so I also wanted to understand 37. So, that number has nagged me ever since, and now this video is being made some 20 years later. - [Derek] Not convinced yet?

- If you take a number that is a multiple of 37 already, like 1, 3, 6, 9, that's 37 squared, and then you reverse it, and then you stick a 0 in between every digit, then that number is a multiple of 37. And I literally spent the next month on the bus trying to prove that fact, which I finally did. Just rattle off a six-digit number.

Tell me any six-digit number. - 413,625. - And it's not divisible by 37.

So how did I figure that out? There's a trick for that. - Is this your like party trick that you can bring out?

- Surprisingly, it doesn't impress as many people as you would think. I think it should impress everybody. - But there's also a practical reason 37 is an important number for humanity.

Say you are faced with a choice that is both immediate and final, like whether to rent the apartment you've just toured or whether to accept a job offer you received. Or it can be as small as whether to stop the next gas station on a road trip. These are all problems where you can't assess all the options at once and then decide.

With each option you encounter, you need to decide whether to accept it or reject it forever and see what comes next. In these scenarios, it feels impossible to make the best choice. If you select too early, you'll probably never even see the best option.

But if you select too late, well, then you've probably rejected the best option already. So your best bet is somewhere in the middle. There, you know at least some information from the options you've seen, and you have some choice, to select or pass.

But how do you know exactly when to decide? The optimal strategy looks like this. First, you need to see some options and reject them automatically just to learn what's out there.

And then at a certain stopping point, S, you need to stop rejecting them and start evaluating whether an option is the best you've seen so far. If it is, then select it. But when should that stopping point be?

We need to work out which stopping point maximizes our chances of picking the best option. We can calculate these chances. For each spot, find the probability that the best option is located there times the probability we get there from stopping point S.

Then, add these probabilities up across every spot. Now, the chance of the best option being in any spot is just random. If there are N options in total, it's 1/N, but it's a little harder to find the chances of getting to each spot.

Say the best option is in the next spot after S, S + 1. What are the chances we get there? Well, since this is the next spot over from the stopping point, we have 100% chance of getting there.

So we are guaranteed to visit it and select it. But if the true best option is in spot S + 2, well, there's a small chance we'll miss it. If the best of all the previous options is sitting in spot S + 1, we would just pick that and stop looking before reaching S + 2.

There's a one in S + 1 chance of this happening. So the chances we do get to spot S + 2 to pick the true best option is 1 minus that, or S over S + 1. This same calculation continues up until the last spot N.

We only get here if we've been passing on every option so far, which means that one of the first S options must have been the best of the total N - 1 options we've seen. In total, this gives us the expression 1/N times 1, + S over S + 1, plus S over S + 2, and so on, all the way up to S over N - 1. Factoring out the S, the sum inside the parentheses approximates the function 1/x going from S to N.

(pensive music) Taking that integral, we get the natural log of N over S. So the probability we select the best option is S over N times the natural log of N over S. To maximize this probability, we can find the peak of this function by setting its derivative to 0, and this gives the natural log of S over N equals -1.

So S over N equals 1 over e, or about 37%. So explore and reject 37% of options just to get a sense of what's out there, and then pick the first option to come along that's better than all of the ones you've seen so far. And your chances of success using this method are also 37%.

(pensive music) This math question is known as the secretary problem or the marriage problem, as it also applies to hiring the best employees or even deciding on the best life partner. Now, it can be impractical to check 37% of the options because you don't always know how many candidates are out there, but the 37% rule also works for time. So if you want to get married, say, in 10 years, then spend the first 3.

7 years seeing what's out there and then select the next person who's better than anyone you've seen. (pensive music) So 37 is actually important to our lives, and people seem to subconsciously recognize this. We gravitate towards the number everywhere.

(pensive music) (film clicking) - 37 seconds. - 37 years. - 37 patties?

- [Speaker 1] I was 37. - [Speaker 2] 37 cubic feet. - [Speaker 3] Take 37.

- [Speaker 4] 37. - How many enemies do you have? - 37.

- 37! - Yes! - [Speaker 5] 37%.

- [Speaker 6] 37. - [Speaker 7] 37. - 37 hours.

- Destroyed 37 restaurants. - 37. - I'm 37.

- 37 interlocking bronze gears. Page 37. 37 years old.

37 prototypes. 37%. (uplifting music) This collection of images, everything you're seeing on screen has been collected by one man over the course of his life.

And you already know who it is. - It's just fun, right? The whole thing is just fun.

How many objects are there here in the room with us that have a 37 on them? This is probably on the order of four digits, I'd say. There's probably not 10,000, but I'm sure there's more than 1,000 here.

Nutri-Grain granola bars, 37 grams. It's a 37-inch yardstick. It's just some political cartoon about sports, but there's no reason that guy had to have Jersey number 37.

A nail that I found somewhere that has 37 on the head. I don't even know what that means. One time, my mom gave me $37 for my birthday.

They all have 37 in the serial number. - Was your 37th birthday like the greatest birthday ever? - I had a big party and I invited everybody I knew.

The Texas state lottery was $37 million. So I had two different friends who both gave me 37 lottery tickets. I didn't win, I won 5 bucks.

This is an article from when they found the 37th Mersenne prime. It's just clipping after clipping. How many hundreds of these do you want me to go through?

I must have gotten that in Germany, but I don't know. . .

But I don't remember what it was. Was it like a locker number? I wouldn't steal a locker number.

I've never stolen for 37. (speaker 1 laughing) - Look at that. Stolen from the highway when I was on a road trip, - [Speaker 1] I heard you say, you never stole anything.

- I have committed a crime. - [Speaker 1] Yes. - There was a bookstore on campus when I was an undergrad at KU, and there were 37 steps in that staircase.

Useful facts, these are useful facts. - Do you feel like everyone gets 37 this much in their lives or do you feel like you're just attracting it? - That's a good question.

You know, the reason I started was because it seemed like it turned up a lot. I started back in the '80s. There was a comedy routine by Charles Fleischer, and he went through this sort of litany of coincidences about the number 37, like there are 37 holes in the speaker part of a telephone.

(jaunty music) Shakespeare wrote 37 plays. There's 37 movements in Beethoven's Nine Symphonies. There are all these amazing coincidences that he rattled off.

I was amazed and I've been collecting them since like 1981. Yeah, so 43? 43 years, probably.

(jaunty music) I built the 37 Website for the first time in 1994. I don't know how the website got out there, but somehow it got out there. I started getting email from strangers.

I've got. . .

Oh, maybe a half a dozen people from around the world, who, every week or month, will post their latest batch of 37s that they've seen out and about. - And they've been doing this for how long? - 18 years.

- Wow. - We're tireless. The tireless cabal of 37 people, yeah.

- Do you have anything to say to anyone who might be like, "37, that's just a base-10 representation of that number. " - I am also interested the number 37 in all of its various other forms: Roman numerals; binary numbers 100101, by the way; numbers in any other base. Yeah, 25 in hexadecimal.

45 in octal. - And do you think you're gonna keep looking for a 37 and collecting 37 for your whole life? - Yeah, yeah, I can't see any reason to stop.

Yeah, for sure. - So maybe there's even something innately universally special about this number. (pensive music) We can argue special coincidences for many numbers, but we need to finally address the elephant in the room.

The sheer amount of brain power 37 secretly takes up in our collective minds. It's humanity's go-to random number, one of our most prominent prime numbers, and most of all, our ideal number for making decisions. Maybe that's why we're inclined to it naturally.

It feels right to us as where to settle and what to pick. Though with this video, we may have ruined randomness even further. I mean, the next time anyone asks people to pick a random number between 1 and 100, more people than ever might be saying, "37.

" (pensive music) - It's been the story of my life that I intend to take everything that I have here and turn them all into individual facts on that website. But the website's been there untouched for 27 years and it hasn't happened. It doesn't look like it's ever gonna happen.

- Maybe on the 37th anniversary, we can get it all done. - That's a good idea. That's a good idea.

Because I have time to do it between now and then, and that would be. . .

That's a great idea. - Once our video comes out, do you want people to write you with any instances they see of 37? You might get swamped, for a little bit.

- 37 is out there, it's everywhere. I'm trying to collect them all. Bring it.

Yes, bring it. (graphic beeping) - Our intuition is one of the most powerful tools we have, and the number 37 is just one example of the unseen patterns in our minds. Luckily, there's a way to supercharge your intuition, giving you the skills to see beyond the everyday and uncover hidden truths about our world.

And you can get started right now for free with this video sponsor, Brilliant. Brilliant gets you hands-on with concepts, in everything from math and data science to programming and technology, to help sharpen your thinking and build your problem-solving skills. On Brilliant, you'll learn by doing.

So even abstract concepts, just click. Plus, you'll be able to take what you learn and apply it to real-world situations. With every lesson, you'll also be building critical thinking skills, training your brain to use your intuition to draw powerful insights.

There's so much to learn on Brilliant. They have thousands of interactive lessons to feed your curiosity. And because each one is bite-sized, it's easy to learn something new, even if you only have a few minutes to spare.

The best part is you can learn from anywhere right on your phone. So wherever you are, you can be building real knowledge and honing your intuition. To try everything Brilliant has to offer for free for 30 days, visit brilliant.

org/veritasium. Scan this QR code or click on the link in the description, and you'll get 20% off Brilliant's annual premium subscription. So I wanna thank Brilliant for sponsoring this part of the video, and I wanna thank you for watching.