The reason why prime numbers are important practically is because of cryptography.
Prime numbers are an essential part of what is called 'public-key cryptography'.
In this technique two (massively massively large) prime numbers are multiplied together to generate a public key. Meanwhile the identity of exactly which two prime numbers are involved is kept secret (this is the private key).
In the system you can use the public key to encode data and send it to me. But only I can decode that data because only I know the private key.
This only works if prime numbers are involved. Otherwise a third party could come along and just start working out all the divisors of my public key and eventually crack which two (non-prime) numbers are the private key.
When prime numbers are used, the third party can still try this method (called a brute force attack) but would have to try loads more numbers (because my public key only has two divisors - the two prime numbers - which by definition have no divisors of their own). This means that it would take a long time and wouldn't really be worth it.
This technique forms the basis of most encryption over the internet (such as https). A website can send out its public key. The web page can then encode data and send it back to the website but it still can't be deciphered without the private key (even if the public key itself was intercepted).
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it helps people answer scientific questions.
so that you know the numbers are the same.
There are certain rules, relationships and formulas that apply and must be understood so that you can use math and numbers to your advantage.
Yes. Hopefully you will encounter numbers sometime in your life, in which you should be able to answer why they are important.
This is told by Carl F. Gauss: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." There are different types of numbers: prime numbers, composite numbers, real numbers, rational numbers, irrational numbers and so on. This study of numbers is included within the concept of maths and numbers and it is very important a study. Therefor number theory holds a greater importance too.