I am afraid the importance is purely intellectual - at least so far. One never knows when a mathematical pursuit will have some practical value. But the reason people do these things is because it is interesting (at least to those who do them!) and is important to other mathematicians. The same thing applies to physicists, too, although there may be more frequent spin-off benefits from some discovery. It may not be readily apparent that there is any practical value in finding the top quark or Higgs boson or in figuring out whether black holes radiate, but that is not why these things are pursued.whatzzupboy said:What is the importance of finding away to descirbe prime numbers in relation to both themselves as well as other numbers?
Although I wasn't aware that prime number theory forms an essential part of encryption theory, that would provide good support for an argument that pure science and mathematics can have a practical spin-off, and so should be supported economically. But I would hate to think that the absence of practical value should deter anyone from the intellectual pursuit of knowledge, or from supporting it economically. Peer review is the proper and best way to ensure that a particular pursuit is worthwhile, not practical usefulness.Gokul43201 said:The relation of primes to composites is all-important. Without knowledge of the unique prime factorization of a number, we would be nowhere in Number Theory. As a result, we would not have public key encryption, and Ebay would not exist.
Of course, it was thought - not too long ago - that Number Theory would have no practical application.
A prime number is a positive integer that is only divisible by itself and 1.
Prime numbers play a fundamental role in number theory and have numerous applications in various branches of mathematics, including cryptography, coding theory, and algebraic geometry. Additionally, prime numbers are essential in understanding the distribution of numbers and have connections to other areas of mathematics, such as the Riemann hypothesis.
In cryptography, prime numbers are used to generate large, secure encryption keys. The security of many encryption algorithms relies on the difficulty of factoring large numbers into their prime factors.
As of 2021, the largest known prime number is 2^82,589,933 − 1, which has over 24 million digits. This number was discovered in December 2018 by the Great Internet Mersenne Prime Search (GIMPS) project.
Prime numbers have numerous practical applications in everyday life, such as in computer security, data encryption, and internet communication. Additionally, prime numbers are used in creating credit card numbers and in generating random numbers for lotteries and games.