Write all the numbers up to 100 and mark the prime numbers. Stop! Do not continue reading! 2 Grab a pencil and a piece of paper. If, at this stage, something excites you and you wish to keep investigating the list of prime numbers and the questions we raised, this means that you have a mathematician’s soul. What does this mean? Do prime numbers become rarer as the numbers grow? Can anyone promise us that we will be able to keep finding more and more prime numbers indefinitely? Another interesting observation is that in each of the first and second groups of 10 numbers (meaning between 1–10 and 11–20) there are four prime numbers, but in the third group of 10 (21–30) there are only two. There are also larger gaps between successive prime numbers, like the six-number gap between 23 and 29 each of the numbers 24, 25, 26, 27, and 28 is a composite number.

In our list, we find successive prime numbers whose difference is exactly 2 (such as the pairs 3,5 and 17,19). So, the distance between any two prime numbers in a row (called successive prime numbers) is at least 2. First, except for the number 2, all prime numbers are odd, since an even number is divisible by 2, which makes it composite. Looking at this short list of prime numbers can already reveal a few interesting observations. In fact, these are the first 10 prime numbers (you can check this yourself, if you wish!). A number that cannot be broken down in this way is called a prime number.

For example, the equations 24 = 4 × 6 and 33 = 3 × 11 show that 24 and 33 are composite numbers. 1Ī whole number that can be written as the product of two smaller numbers is called a composite number. With a compass and protractor as the only available instruments, division of a circle into equal sectors had great practical value. In ancient times, dividing a circle into equal-sized sectors with high precision was necessary for various artistic, astronomical, and engineering purposes. If the circle is divided into two, three, four, ten, twelve, or thirty equal parts, each part will contain a whole number of degrees and there are additional ways of dividing a circle that we did not mention. This is also the reason why the circle was divided into 360°. In a factory that works non-stop in 8-h shifts, each day is divided into exactly three shifts. This means that a day can be divided into two equal parts of 12 h each, daytime and nighttime. For example, 24÷2 = 12, 24÷3 = 8, 24÷4 = 6, and so on (complete the rest of the options yourself!). Have you ever wondered why the day is divided into exactly 24 h, and the circle into 360 degrees? The number 24 has an interesting property: it can be divided into whole equal parts in a relatively large number of ways. In this short paper, we will try to follow the history of prime numbers since ancient times and use this opportunity to dive into and better understand the mathematician’s world. On a small scale, the appearance of prime numbers seems random, but on a large scale there appears to be a pattern, which is still not fully understood. What are they? Why are the questions related to them so hard? One of the most interesting things about prime numbers is their distribution among the natural numbers. We explain what they are, why their study excites mathematicians and amateurs alike, and on the way we open a window to the mathematician’s world.įrom the beginning of human history, prime numbers aroused human curiosity. Prime numbers have attracted human attention from the early days of civilization.