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    Factorization is not efficient, even though an effective ... — Carmelics
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    Factorization is not efficient, even though an effective procedure for it exists

    CausationTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Multiplication conserves information, making it reversible to some extent
      ?

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    • 2.Finding the unique set of primes for a natural number n is called factorization
      ?

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    • 3.An effective procedure exists: try dividing n by all numbers between 1 and √n
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Efficiency is not an intrinsic property of a problem but is relative to computational model, input encoding, and available resources.
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    • 2.The claim conflates trial division (one inefficient algorithm) with factorization as a class, ignoring sub-exponential methods like the general number field sieve.
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    • 3.Since no proof exists that factorization lacks a polynomial-time algorithm, asserting it is 'not efficient' asserts an unresolved conjecture as established fact.
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    Reason against 2 of 2
    ?
    • 1.Church-Turing thesis variants (e.g., the efficient Church-Turing thesis) are contested, meaning what counts as 'effective' versus 'efficient' may not be sharply distinguishable.
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    • 2.Shor's quantum algorithm solves integer factorization in polynomial time, demonstrating that efficiency is model-dependent, not inherent to the problem's logical structure.
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    Related

    An effective procedure exists: try dividing n by all numbers between 1 and √nChurch-Turing thesis variants (e.g., the efficient Church-Turing thesis) are con...Efficiency is not an intrinsic property of a problem but is relative to computat...Finding the unique set of primes for a natural number n is called factorization
    +5 moreShow less
    Multiplication conserves information, making it reversible to some extentShor's quantum algorithm solves integer factorization in polynomial time, demons...Since no proof exists that factorization lacks a polynomial-time algorithm, asse...Such trial-division techniques are not efficientThe claim conflates trial division (one inefficient algorithm) with factorizatio...

    Similar

    Infinitesimal methods are more efficient than alternative approaches78%A non-terminating procedure does not qualify as effective.73%Extensive effort has been devoted to finding efficient solutions for p...73%Extensive effort has been devoted to finding efficient solutions for N...72%

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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
    Extraction notes

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    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit