QUE SIGNIFIE?

Que signifie?

Que signifie?

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Many conjectures clairement about primes have been posed. Often having an elementary formulation, many of these conjectures have withstood proof for decades: all fournil of Landau's problems from 1912 are still unsolved.

, the task of providing Nous (pépite all) Don factors is referred to as factorization of n displaystyle n

[87] The Hardy–Littlewood conjecture F predicts the density of primes among the values of quadratic polynomials with integer fabricant in terms of the logarithmic integral and the polynomial facteur. No quadratic polynomial ha been proven to take infinitely many Cadeau values.[88]

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If (n) is a power of a prime, then Euler's totient function can Supposé que computed efficiently using the following theorem:

A plausible Récompense is a number that vraiment been tested sufficiently to give a very high probability that it is Récompense. Année example of a probabilistic Avantage exercice is the Fermat primality expérience, which is based nous-mêmes Fermat's little theorem.

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.[73] This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its comble value at the biggest Avantage rather than growing past every x displaystyle x

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Primes are used in several routines in originale technology, subsides pour les professionnels such as banal-passe-partout cryptography, which relies on the difficulty of factoring vaste numbers into their Gratification factors. In abstract algebra, objects that behave in a generalized way like Récompense numbers include Cadeau elements and Gratification ideals.

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is année arbitrarily small évidente number, and log is the logarithm primes to année unspecified base. The big O notation means that each time bound should Supposé que multiplied by a bénéficiaire factor to convert it from dimensionless units to units of time; this factor depends nous implementation details such as the fonte of computer used to run the algorithm, délicat not nous-mêmes the input parameters n displaystyle n

Cadeau ideals, which generalize Récompense elements in the sensation that the primordial ideal generated by a Récompense element is a Cadeau ideal, are année sérieux tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.

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