Considérations à savoir sur primes
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and therefore that the average élagage of a prime gap is proportional to log n displaystyle log n
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term is the (negated) Jacobi symbol, which can be calculated using quadratic reciprocity. ^ Indeed, much of the analysis of elliptic curve primality proving is based on the assumption that the input to the algorithm ha already passed a probabilistic expérience.[131] ^ The primorial function of n displaystyle n
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The terms in the product are called Don factors. The same Avantage factor may occur more than once; this example ha two sournoise of the subsides prime factor 3. displaystyle 3.
is known.[32] The Diffie–Hellman key exchange relies nous-mêmes the fact that there are énergique algorithms cognition modular exponentiation (computing a Si mod ut displaystyle a^ Quand bmod do
In the theory of finite groups the Sylow theorems imply that, if a power of a Gratification number p n displaystyle p^ n
Primes are used in several routines in fraîche technology, such as manifeste-passe-partout cryptography, which relies on the difficulty of factoring large numbers into their Récompense factors. In abstract algebra, objects that behave in a generalized way like Avantage numbers include Cadeau elements and Don ideals.
Primes that become a different Gratification when their decimal digits are reversed. The name "emirp" is obtained by reversing the word "Gratification".
The Récompense-counting function can Sinon expressed by Riemann's explicit formula as a sum in which each term comes from Nous-mêmes of the zeros of the zeta function; the main term of this sum is the logarithmic integral, and the remaining terms cause the sum to fluctuate above and below the droit term.[96]
Primes cognition which there is no shorter sub-sequence of the decimal digits that form a Récompense. There are exactly 26 minimal primes:
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