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kerimek
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Does exist any proof that prime numbers cannot be generated sequentially without jump across any one? And which is cardinality of prime numbers set? Is the set "the smallest" infinite set?
Originally posted by Hurkyl
There does actually exist an explicit (but complicated) formula for the n-th prime number.
Originally posted by kerimek
Does exist any proof that prime numbers cannot be generated sequentially without jump across any one? And which is cardinality of prime numbers set? Is the set "the smallest" infinite set?
Prime numbers are positive integers that are divisible only by 1 and themselves. They have exactly two factors, 1 and the number itself.
Prime numbers have many important applications in fields like cryptography, computer science, and mathematics. They are also used in algorithms for solving various problems.
There are various methods for searching for prime numbers, such as using sieves, algorithms, and mathematical formulas. Some commonly used algorithms include the Sieve of Eratosthenes and the AKS primality test.
No, the search for prime numbers is an ongoing process as there is no limit to the number of prime numbers. As numbers get larger, it becomes more difficult to find new primes, but there will always be more to discover.
Yes, prime numbers have many practical applications, such as in encryption algorithms used to secure online transactions and protect sensitive information. They are also used in creating unique identification numbers and in generating random numbers for various applications.