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  1. The prime symbol ′ is commonly used to represent feet (ft), and the double prime ″ is used to represent inches (in). [2] The triple prime ‴, as used in watchmaking, represents a ligne ( of a "French" inch, or pouce, about 2.26 millimetres or 0.089 inches). [3] Primes are also used for angles. The prime symbol ′ is used for arcminutes ...

  2. Dec 12, 2006 · to and including p. Therefore, it is either prime or divisible by a prime between p and q. In the first case, q is a prime greater than p. In the second case, the divisor of q between p and q is a prime greater than p. Then for any prime p, this construction gives us a prime greater than p. Thus, the number of primes must be infinite [4].

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  4. 3 days ago · A symbol used to distinguish a third quantity x^('') ("x double prime") from two other related quantities x and x^' ("x prime). Double primes are most commonly used to denote transformed coordinates, conjugate points, and derivatives. A double prime is also used to denote the number of arc seconds in an angle measure, or the number of inches in a length.

  5. converges to a definite number ("Brun's constant"), which expresses the scarcity of twin primes, even if there are infinitely many of them (Ribenboim 1996, p. 201).By contrast, the series of all prime reciprocals diverges to infinity, as follows from the Mertens second theorem by letting .

  6. double prime: [noun] the symbol ″ used to distinguish arbitrary characters (such as a, a′, and a″), to indicate a specific unit (such as inches), or to indicate the second derivative of a function (such as p″ or f″(x)) — compare prime 7.

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