How to tell if a number is prime?
Could you please elaborate on the process of determining whether a given number is prime or not? I'm particularly interested in understanding the steps involved and any specific techniques or algorithms that might be used for this purpose. Could you also explain how we can efficiently check for primality, especially for large numbers? Additionally, are there any common mistakes or pitfalls that people often encounter when trying to determine primality? I would appreciate it if you could provide a clear and concise explanation.
What is the mining of prime number?
Could you please elaborate on the concept of prime number mining? Could you explain how the process works, what its purpose is, and perhaps some of the challenges involved in this endeavor? Additionally, I'm curious to know if prime number mining has any real-world applications or if it's solely a mathematical pursuit. Finally, I'd like to understand if there are any specific tools or technologies required for prime number mining and if it's accessible to the general population.