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A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
A prime number (or prime) is a ... Mathematics portal; ... All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages.
All instances of log (x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln (x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they ...
A simple formula is. for positive integer , where is the floor function, which rounds down to the nearest integer. By Wilson's theorem, is prime if and only if . Thus, when is prime, the first factor in the product becomes one, and the formula produces the prime number . But when is not prime, the first factor becomes zero and the formula ...
An odd prime number p is defined to be regular if it does not divide the class number of the p th cyclotomic field Q (ζp), where ζp is a primitive p th root of unity. The prime number 2 is often considered regular as well. The class number of the cyclotomic field is the number of ideals of the ring of integers Z (ζp) up to equivalence.
Bertrand's postulate. In number theory, Bertrand's postulate is the theorem that for any integer , there exists at least one prime number with. A less restrictive formulation is: for every , there is always at least one prime such that. Another formulation, where is the -th prime, is: for.
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