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Why is it so difficult to predict prime numbers?
And has Riemann's conjecture been solved yet?
And has Riemann's conjecture been solved yet?
chingkui said:There are many questions about Riemann Hypothesis I always like to ask about:
1) I always hear that RH is important in providing information to the distribution of prime. In particular, how important is it? Why is the distribution of zeros of a function so important? I heard that prime distribution behave nicely if RH is true, but what is meant by "nice"? What if RH turn out to be false? How "badly" will prime distribution behave?
chingkui said:2) Let say if RH fail to be true, does anyone know if it would fail for only finitely many points or infinitely many points? Does the "bad" behavior of prime distribution depend on where the RH fail? Will the "bad behavior" behave "nicer" if RH fail only at small number of points? And does it depend on the magnitude of the complex part of the failed points?
Prime numbers are numbers that are only divisible by 1 and themselves. They have no other factors.
Predicting prime numbers is important in mathematics and cryptography. Prime numbers are the building blocks of many mathematical concepts and are used in encryption algorithms to keep data secure.
There are many different methods for predicting prime numbers, including the Sieve of Eratosthenes, the Sieve of Sundaram, and the Miller-Rabin primality test. These methods use various algorithms and mathematical equations to determine whether a number is prime.
While there is no simple formula for predicting prime numbers, there are patterns and rules that can help identify prime numbers. However, these patterns are not foolproof and cannot predict all prime numbers.
No, it is not possible to predict prime numbers infinitely. As the numbers get larger, it becomes increasingly difficult to accurately predict whether a number is prime or not. Therefore, there is no way to predict all prime numbers with complete certainty.