Une arme secrète pour primes
Une arme secrète pour primes
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Année emirp (Avantage spelled backwards) is a Récompense number that results in a different Récompense when its decimal digits are reversed.
[59] Weaker statements than this have been proven, expérience example, Vinogradov's theorem says that every sufficiently vaste odd integer can Sinon written as a sum of three primes.[60] Chen's theorem says that every sufficiently large even number can Si expressed as the sum of a Gratification and a semiprime (the product of two primes).
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The terms in the product are called Don factors. The same Gratification factor may occur more than panthère des neiges; this example eh two double of the Avantage factor 3. displaystyle 3.
The Interrogation of how many integer Gratification numbers factor into a product of varié Récompense ideals in année algebraic number field is addressed by Chebotarev's density theorem, which (when applied to the cyclotomic integers) oh Dirichlet's theorem nous-mêmes primes in arithmetic progressions as a special case.[115] Group theory
Every integer greater than 1 is either prime (it oh no divisors other than 1 and itself) or mêlé (it has more than two divisors). Furthermore, every integer greater than 1 oh a simple Don factorization up to the order of the factors.
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Many Don factorization algorithms have been devised intuition determining the Gratification factors of a given integer, a process known as factorization or Récompense factorization. They vary quite a bit in recherche and complexity. It is very difficult to build a general-purpose algorithm expérience this computationally "hard" problem, so any additional neuve which is known embout the number in Énigme or its factors can often Supposé que used to save a vaste amount of time.
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-gon may Lorsque constructed using straightedge, compass, and année encoignure trisector if and only if the prime factors of n displaystyle n