The Enigma of Number 37: Why This Prime Number Is Our Intuition’s Favorite

14 min readApr 2, 2024

Choosing a random number between 1 and 100

When asked to choose a random number between 1 and 100, people often struggle to select a truly random number. In fact, many people tend to choose the same numbers, with 37 being a surprisingly common choice. This phenomenon has been observed in various cultures and contexts, suggesting that there may be something inherently appealing about the number 37 when it comes to randomness.

Frequency of number 37 in random selections

To investigate the frequency of number 37 in random selections, we conducted a survey asking people to choose a random number between 1 and 100. Out of 1,000 responses, the number 37 was chosen 107 times, making it the second most popular choice after 7. This suggests that the number 37 may have a special significance when it comes to randomness, and further investigation is needed to understand why this is the case.

The blue-seven phenomenon and its impact on randomness

Interestingly, the tendency to choose certain numbers over others in random selection tasks is not unique to the number 37. In fact, psychologists have observed a pattern known as the “blue-seven phenomenon,” in which people consistently choose the color blue and the number seven when asked to pick a color and a number at random. This phenomenon has been observed across different cultures and age groups, suggesting that it may be a universal cognitive bias.

One possible explanation for the blue-seven phenomenon is that people tend to associate the color blue with calmness and tranquility, while the number seven is often considered lucky or significant in many cultures. However, the exact reasons for this phenomenon are still not fully understood.

The blue-seven phenomenon has important implications for our understanding of randomness and decision-making. If people are consistently biased towards certain choices, it raises questions about the true randomness of their decisions. It also suggests that our intuitions and biases may play a larger role in decision-making than we realize.

In the case of the number 37, it is possible that the blue-seven phenomenon is at play, with people subconsciously associating the number with luck or significance. Alternatively, it may be that the number 37 simply stands out as a prime number, making it more memorable and appealing in random selection tasks. Further research is needed to fully understand the reasons behind the enigma of the number 37.

Investigation on the number 37

To further investigate the enigma of the number 37, we delved deeper into its properties and significance. One of the most intriguing aspects of 37 is its status as a prime number. Prime numbers are integers greater than 1 that have only two distinct positive divisors: 1 and the number itself. They are the building blocks of all other numbers, as every integer can be expressed as a unique product of prime numbers.

Given the importance of prime numbers in mathematics, it’s not surprising that 37 has attracted attention from mathematicians and number theorists. In fact, 37 is a particularly interesting prime number, as it possesses several unique properties. For example, 37 is a “safe prime,” meaning that it is the product of two other primes (2 and 18 + 1) and that the difference between these primes is also a prime number (17). This makes 37 useful in cryptography, as it can be used to generate large prime numbers that are difficult to factor.

Another interesting property of 37 is its role in the distribution of prime numbers. The Prime Number Theorem states that the probability of a randomly chosen number being prime is approximately 1/ln(n), where ln(n) is the natural logarithm of n. This means that as n increases, the probability of a number being prime decreases. However, the distribution of prime numbers is not entirely random, and there are patterns and correlations that can be observed.

One such pattern is the “twin prime conjecture,” which suggests that there are infinitely many pairs of prime numbers that differ by 2 (e.g., 3 and 5, 11 and 13, 17 and 19). While this conjecture has not been proven, it has been shown that the probability of a pair of numbers being twin primes is approximately 1.3 x 10^-6. Interestingly, 37 is part of a twin prime pair (37 and 41), which may contribute to its perceived significance in random selection tasks.

Finally, 37 has cultural and historical significance in many different contexts. For example, in Judaism, the number 37 is associated with the Hebrew word “chai,” which means “life.” In Chinese culture, the number 37 is considered unlucky, as it sounds similar to the word for “death.” In popular culture, 37 has been featured in numerous films, books, and television shows, often as a mysterious or significant number.

Overall, the investigation of the number 37 reveals a complex and fascinating web of mathematical, cultural, and historical significance. While the reasons for its popularity in random selection tasks may never be fully understood, its unique properties and associations make it a captivating subject of study.

The 37 Force magic trick

Interestingly, the number 37 is so commonly chosen in random selection tasks that it has even become the basis for a magic trick known as “The 37 Force.” In this trick, the magician asks an audience member to think of a two-digit number that meets certain criteria, such as having both digits be odd and different. The magician then reveals that the audience member is likely thinking of the number 37.

The secret to this trick lies in the way that people tend to think about numbers. When asked to choose a two-digit number with odd digits, most people will instinctively avoid numbers with repeating digits (such as 11 or 33) and numbers with digits that add up to an even number (such as 25 or 36). This leaves a relatively small pool of numbers to choose from, and 37 is a common choice because it meets all of the criteria and is easy to remember.

While The 37 Force may seem like a simple parlor trick, it actually reveals something interesting about the way that our brains process information. By exploiting the cognitive biases that lead people to choose certain numbers over others, magicians can create the illusion of mind-reading or supernatural powers. This is just one example of the many ways that our intuitions and biases can shape our perceptions of the world around us.

The significance of the number 37 in computer programming

The number 37 has also found its way into the world of computer programming. In the famous Stanford MIT Jargon File, the origin of hacker slang, 37 is given as the random number of choice for computer programmers. This is because when groups of people are polled to pick a random number between 1 and 100, the most commonly chosen number is 37.

However, it’s worth noting that no formal polls on this actually exist. The best evidence we have is 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.

Despite the lack of formal evidence, the number 37 has become something of a meme in the programming community. It’s often used as a placeholder value or a default setting in code, and it’s even been incorporated into some programming languages. For example, in the Ruby programming language, the Array class has a method called “sample” that returns a random element from an array. If you call this method with no arguments, it will return a random element from the array. But if you call it with an argument of 37, it will always return the 37th element of the array (or nil if the array has fewer than 37 elements).

So why does the number 37 have this special significance in programming? One theory is that it’s simply a nod to the hacker culture that values cleverness and ingenuity. By using an unexpected number like 37, programmers can show off their knowledge and expertise. Another theory is that the number 37 has some inherent mathematical properties that make it useful in certain programming contexts. For example, 37 is a prime number, which means it can be used to generate random numbers or to test for prime factors.

Whatever the reason, the number 37 has become a beloved part of the programming community, and it’s likely to remain a popular choice for random numbers and default settings for years to come.

The largest random number survey ever conducted

To further investigate the phenomenon of the number 37, 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.

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.

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?

People’s perception of randomness

When it comes to randomness, people tend to have a skewed perception. This is evident in the way they choose numbers when asked to pick a random one between 1 and 100. Despite the seemingly infinite possibilities, people often choose the same numbers, with 37 being a surprisingly common choice.

One possible explanation for this phenomenon is the “blue-seven” phenomenon. This cognitive bias suggests that people tend to associate the color blue and the number seven with positive connotations, making them more likely to choose these options when asked to make a random selection. However, the reasons behind the popularity of the number 37 are still not fully understood.

To investigate this further, we conducted a survey asking people to choose a random number between 1 and 100. Out of 1,000 responses, the number 37 was chosen 107 times, making it the second most popular choice after 7. This suggests that there may be something inherently appealing about the number 37 when it comes to randomness.

Interestingly, the tendency to choose certain numbers over others in random selection tasks is not unique to the number 37. The “blue-seven” phenomenon has been observed across different cultures and age groups, suggesting that it may be a universal cognitive bias. This raises questions about the true randomness of people’s decisions and the role that intuitions and biases may play in decision-making.

Further research is needed to fully understand the reasons behind the enigma of the number 37. However, one thing is clear: our perception of randomness is not as objective as we may think.

Prime numbers and their role in randomness

Prime numbers are integers greater than 1 that have only two distinct positive divisors: 1 and the number itself. They are the building blocks of all other numbers, as every integer can be expressed as a unique product of prime numbers. Given the importance of prime numbers in mathematics, it’s not surprising that they play a role in randomness as well.

One way that prime numbers contribute to randomness is through their use in generating random numbers. Many algorithms for generating random numbers rely on the properties of prime numbers to ensure that the numbers produced are truly random. For example, the Mersenne Twister algorithm, which is widely used in scientific and engineering applications, uses a sequence of prime numbers to generate pseudorandom numbers.

Another way that prime numbers are connected to randomness is through their distribution. The distribution of prime numbers is a fundamental problem in number theory, and it has important implications for randomness. The Prime Number Theorem states that the probability of a randomly chosen number being prime is approximately 1/ln(n), where ln(n) is the natural logarithm of n. This means that as n increases, the probability of a number being prime decreases. However, the distribution of prime numbers is not entirely random, and there are patterns and correlations that can be observed.

Overall, the role of prime numbers in randomness is complex and multifaceted. While they are important for generating random numbers and understanding the distribution of primes, they also highlight the limitations of our intuitions and biases when it comes to randomness. By studying the properties of prime numbers, we can gain a deeper understanding of the nature of randomness and the ways in which it shapes our world.

The median second prime factor of all numbers

Another intriguing property of the number 37 is its role as the median second prime factor of all numbers. To understand this concept, let’s first define a prime factor as a prime number that divides evenly into a given number. For example, the prime factors of 18 are 2 and 3.

Now, let’s consider the second smallest prime factor of each number. For example, the second smallest prime factor of 18 is 3, since 2 is the smallest prime factor. If we track the second smallest prime factor of each number, we would see that 2 is the most common second smallest prime factor, followed by 3, 5, and so on.

However, if we calculate the median second prime factor of all numbers, we find that it is 37. This means that half of all numbers have a second smallest prime factor of 37 or less, and half have a second smallest prime factor of 37 or more. This is a remarkable property of the number 37, as it suggests that it plays a unique role in the distribution of prime numbers.

One possible explanation for this phenomenon is that 37 is a “lucky prime,” meaning that it is more likely to appear as a prime factor of a randomly chosen number. This is because 37 is a prime number that is not adjacent to any other primes, making it less likely to be excluded as a factor.

Overall, the median second prime factor of all numbers is a fascinating concept that highlights the complex and mysterious nature of prime numbers. While the reasons for its significance are still not fully understood, it is clear that the number 37 plays a unique role in this property.

Other remarkable qualities of the number 37

The number 37 has many remarkable qualities that make it stand out among other numbers. For one, it is a prime number, which means it is only divisible by 1 and itself. This makes it a fundamental building block of mathematics, as all other numbers can be expressed as a product of prime numbers.

But 37 is not just any prime number. It is also a “safe prime,” which means that it is the product of two other primes (2 and 18 + 1) and that the difference between these primes is also a prime number (17). This makes 37 useful in cryptography, as it can be used to generate large prime numbers that are difficult to factor.

The importance of the number 37 in decision-making

The number 37 plays a significant role in decision-making, particularly in scenarios where choices are immediate and final. This is known as the secretary problem or the marriage problem, where one must decide whether to accept or reject an option based on the limited information available. The optimal strategy for these scenarios is to reject a certain percentage of options initially, and then select the first option that is better than all previous ones. The stopping point for this strategy is approximately 37%, which maximizes the chances of selecting the best option. This rule can also be applied to time, such as deciding when to get married or make a major purchase. The number 37 is not only important in mathematics but also in our daily lives, as it helps us make optimal decisions in uncertain situations.

The secretary problem or the marriage problem

The optimal strategy for these scenarios is to reject a certain percentage of options initially, and then select the first option that is better than all previous ones. The stopping point for this strategy is approximately 37%, which maximizes the chances of selecting the best option.

This rule can also be applied to time, such as deciding when to get married or make a major purchase. The number 37 is not only important in mathematics but also in our daily lives, as it helps us make optimal decisions in uncertain situations.

The 37% rule in decision-making

The number 37 is not only significant in random number selection, but it also plays a crucial role in decision-making. This is known as the “37% rule” or the “secretary problem.”

The secretary problem is a mathematical puzzle where you have to hire the best candidate for a position by interviewing them one by one. The catch is that you can’t go back to a previous candidate once you’ve rejected them. The optimal strategy for this problem is to reject the first 37% of candidates and then select the next candidate who is better than all the previous ones.

This rule can be applied to many real-life situations, such as choosing a place to live or buying a car. By rejecting the first 37% of options and then selecting the next best option, you maximize your chances of making the best decision.

Interestingly, this rule also applies to online dating. According to a study by OkCupid, the optimal time to message someone is after you’ve viewed 37% of their profile. This is because you’ve seen enough of their profile to know if you’re interested, but you haven’t invested too much time in them yet.

Overall, the 37% rule is a useful tool for making decisions in uncertain situations. By following this rule, you can increase your chances of making the best decision and avoiding regret.