9 Answers

New AnswerPrimes are important for encryption and public/private key ciphers. This is due in part to the mathematical properties of multiplicative groups, when using prime numbers this will give a system that can encrypt and decrypt properly (this is not guaranteed for composite numbers). Also, because they are prime, they have only 2 factors which makes it really difficult to crack it. RSA ciphers use the product of two large primes in the algorithm. Finding larger and larger primes is obviously of interest, because big primes are hard to find and to crack. Having an understanding of the principles and their use in encryption is probably the best way to win your bread with primes

Since the late 20th century, with the help of computers, prime numbers with millions of digits have been discovered (--> Mersenne number!:). Like efforts to generate ever more digits of π, such number theory research was thought to have no possible application - that is, until cryptographers discovered how large primes could be used to make nearly unbreakable codes (--> cryptology: Two - key cryptography!:) https://www.sololearn.com/post/20122/?ref=app

All the important things are consequences of Arithmetic's Fundamental theorem (known also as "Z is an UFD")

Primes are of the utmost importance to number theorists because they are the building blocks of whole numbers, and important to the world because their odd mathematical properties make them perfect for our current uses. You can also understand by watch this 2minutes video>>> https://youtu.be/qQYeYyM1k9o

prime numbers are helpful to prevent collisions in modulo operations which are heavily used in encryption and hashing algorithms.