Prime Numbers (1 Viewer)

[vtx]

Why are prime numbers so important in higher level maths? The most difficult analysis questions in maths olympiads usually involve primes, the Riemann Hypothesis is about primes, questions on Project Euler have a strong insistence on primes and algorithms to compute large primes efficiently. etc. What are their applications in the real world?

 

[GoldyOrNugget]

One place where they're used extensively is cryptography. It is very easy to compute the multiplication of two large primes; it is very difficult to factor the multiplication of two large primes. Most secure systems use prime-based encryption algorithms like RSA.

 

[seanieg89]

Cryptography is probably their most important "real world" application as Goldy said.

From the perspective of pure mathematics they are important simply because they are the multiplicative "building blocks" of the natural numbers, and although they have been studied for thousands of years, there are still lots of conjectures about them that are very simple to state but we are nowhere near proving (such as Goldbach's conjecture). They are very mysterious and beautiful for objects whose definition can be explained to a primary school child.