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    Such trial-division techniques are not efficient — Carmelics
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    Supports→Factorization is not efficient, even though an effective procedure for it exists

    Such trial-division techniques are not efficient

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    Related propositions within the same area of thought.
    An effective procedure exists: try dividing n by all numbers between 1 and √nFactorization is not efficient, even though an effective procedure for it existsFinding the unique set of primes for a natural number n is called factorizationMultiplication conserves information, making it reversible to some extent

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    Trial division requires at most n trials to find a factor of n76%Infinitesimal methods are more efficient than alternative approaches72%Factorization is not efficient, even though an effective procedure for...72%No existing method has succeeded in yielding the desired separations69%

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    (In)efficiency of Factorization. Since multiplication conserves information the function is, to an extent, reversible. The process of finding the unique set of primes for a certain natural number n is called factorization. Observe that the use of the term “only” in the definition of a prime number implies that this is in fact a negative characterization: a number n is prime if there exists no number between 1 and n that divides it. This gives us an effective procedure for factorization of a numb

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