# Why are prime numbers important in real life? [duplicate]

What practical use are prime numbers? Why do we emphasise the teaching of prime numbers?

## marked as duplicate by William, Raskolnikov, Start wearing purple, user1337, Dan RustSep 3 '13 at 10:31

• Your question isn’t really very clear. What context do you have in mind when you say that we emphasize the teaching of prime numbers? – Brian M. Scott Sep 3 '13 at 9:31
• Cryptography is the only "practical use" that comes to mind. – daniel Sep 3 '13 at 9:46
• To continue Brian's question (into possibly a different direction what he had in mind): at what level are you being taught about prime numbers? Knowing that helps answering your question. – Jyrki Lahtonen Sep 3 '13 at 9:51

For mathematics in general, the value of prime numbers lies much deeper. For example, the distribution of prime numbers encodes very deep mathematical information in general (not only via the Riemann Hypothesis). Completions of the rational numbers naturally lead to $p$-adic fields, and the idea of being "prime" applies to many other structures (like prime ideals, prime geodesics etc.). So we emphasise teaching prime numbers because they lie at the very heart of mathematics.