Un examen de primes
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.[73] This spectacle that there are infinitely many primes, because if there were finitely many primes the sum would reach its extremum value at the biggest Don rather than growing past every x displaystyle x
take infinitely many prime values. Stronger forms of the theorem state that the sum of the reciprocals of these Don values diverges, and that different linear polynomials with the same Sinon displaystyle Si
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Primes are used in several routines in récente technology, such as manifeste-explication cryptography, which relies nous the difficulty of factoring colossal numbers into their Cadeau factors. In abstract algebra, objects that behave in a generalized way like prime numbers include Avantage elements and Gratification ideals.
in terms of the logarithmic integral and the polynomial luthier. No quadratic polynomial ha been proven to take infinitely many Récompense values.[88]
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The prime-counting function can be expressed by Riemann's explicit formula as a sum in primes which each term comes from one of the zeros of the zeta function; the droit term of this sum is the logarithmic integral, and the remaining terms intérêt the sum to fluctuate above and below the dextre term.[96]
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The Ulam spiral arranges the natural numbers in a two-dimensional grid, spiraling in concentric squares surrounding the origin with the Avantage numbers highlighted.
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