how are prime numbers useful?

Question

need help with math essay

Answer 1

While extremely important in mathematics, prime numbers find applications outside mathematics mostly in cryptography and security systems, and also for psuedo-random number generation.

Answer 2

If you're looking for a direction go go with an essay consider this: we know lots and lots of primes. 1, 2, 3, 5, 7, and so on for a long time. However, if you look at the largest prime known to man right now, knowing that does not help us know what the NEXT prime number after that is. They don't seem to be spread along the number line in any coherent fashion so the only way to find the next prime is to actually check each and every number until you find one. This means that finding the prime factorization of a very large number is, for lack of a better word, hard. Even with a computer. Because it's so difficult, the factorization of large numbers that are the products of two huge primes is the basis for much of out online/telephone/banking/etc security. It's called public key cryptography and it is effective because finding the prime factorization of a large number (hundreds of digits long) is too time consuming. If anyone figures out a way, they'll rule the world. Or at least the online/telephone/banking part of it. ;)

Answer 3

To be a bit vague, prime numbers seem to be fairly meaningless outside of number theory. But they do have at least one practical application that I know of.

Prime numbers, specifically the product of two large prime numbers, is the key to a popular method of encryption called RSA public/private keys. I don't know how much you know about encryption, but you should know it's a way of for two people to send their messages as numbers that are meaningless to everybody but themselves. In other words, encryption is a way of keeping a message secret from eaves droppers even when the eaves droppers can read the entire encrypted message.

I know for a fact that RSA security has been implemented in thousands of credit readers, and it is prime numbers
...(specifically the ease at which we can generate the product of two large prime numbers and the impractically difficult problem of factoring someone else's product of their two secret prime numbers)...
that prevents your credit card numbers from being readable by any nosy eaves droppers.

So in a sense, prime numbers today are working hard protecting millions of credit card numbers every day.