Language isolateA language isolate is a language that has no demonstrable genetic relationship with another language. Basque in Europe, Ainu in Asia, Sandawe in Africa, Haida in North America, Kanoê in South America, and Tiwi in Australia are all examples of language isolates. The exact number of language isolates is yet unknown due to insufficient data on several languages. One explanation for the existence of language isolates is that they might be the last remaining branch of a larger language family.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Languages of AfricaThe number of languages natively spoken in Africa is variously estimated (depending on the delineation of language vs. dialect) at between 1,250 and 2,100, and by some counts at over 3,000. Nigeria alone has over 500 languages (according to SIL Ethnologue), one of the greatest concentrations of linguistic diversity in the world. The languages of Africa belong to many distinct language families, among which the largest are: Niger–Congo, which include the large Atlantic-Congo and Bantu branches in West, Central, Southeast and Southern Africa.
Prime numberA 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 product (2 × 2) in which both numbers are smaller than 4.
Formula for primesIn number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be. 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 .
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