Unfortunately, there is no known formula to generate all prime numbers. Prime numbers have been the subject of much mathematical investigation and while there are patterns that have been discovered, the distribution of primes is not truly random. The Prime Number Theorem states that the distribution of primes becomes more random as they get larger, but this is only an approximation and is not exact. Nevertheless, there are various algorithms and theories, such as the Sieve of Eratosthenes and the Riemann Hypothesis, that help us understand the distribution of primes to a certain extent.
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