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    Home/Original/inverse
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    Inverse View

    It is not the case that The AKS verification of primality operates on the bit-length of each factor, but the product of these lengths can grow super-polynomially relative to the input encoding of n.

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    Reasons For

    1 perspective
    Reason for
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    • 1.AKS runtime is proven polynomial in log(n)—O((log n)⁶) or O((log n)⁴) with improvements—making super-polynomial growth impossible by definition.
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    • 2.A product of factor bit-lengths is still bounded by O((log n)²), not exceeding the polynomial bound relative to input encoding length.
      ?

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    • 3.The claim conflates bit-operations on individual factors with overall algorithmic complexity, which must remain polynomial for AKS correctness.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.AKS checks divisibility by polynomials over Z/nZ, requiring bit operations proportional to log(n)² or higher per polynomial test.
      ?

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    • 2.The number of distinct prime power factors can be O(log n), and encoding each factor's bit-length independently yields multiplicative complexity.
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    • 3.Complexity analysis distinguishes between input size (log n bits) and actual computational work across factor encodings, which can diverge.
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