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. n is a natural number (including 0) in the definitions. More details are in the article for the name. Lists of primes by typeīelow are listed the first prime numbers of many named forms and types. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2 ×10 22) below 10 24, if the Riemann hypothesis is true.
There are known formulae to evaluate the prime-counting function (the number of primes below a given value) faster than computing the primes.
List of prime numbers up to 100 verification#
The Goldbach conjecture verification project reports that it has computed all primes below 4×10 18. The following table lists the first 1000 primes, with 20 columns of consecutive primes in each of the 50 rows.
2.30.5 Other generalizations and variations.2.12.1 Euler ( p, p − 3) irregular primes.2.9 Eisenstein primes without imaginary part.