Unverified50% confidenceFactExact time
The academic community conjectures that the optimal complexity lower bound for integer multiplication is Ω(n log n), but this has not been rigorously proved to date and remains an empirical conjecture.
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50%
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Long-term
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10/7/2026
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Related Claims
UnverifiedQuicksort has an average time complexity of n log n and degrades to O(n²) in the worst case.75% similarUnverifiedThe Schönhage–Strassen algorithm leverages the Fast Fourier Transform (FFT) to reduce integer multiplication complexity to O(n log n log log n).69% similarUnverifiedShor算法将整数分解的复杂度从经典的亚指数级降至多项式级O((log N)³)67% similarUnverifiedNTT (Number Theoretic Transform) can reduce the complexity of polynomial multiplication from O(n²) to O(n log n).67% similarUnverifiedWhen using exact rational arithmetic, the bit length of intermediate rational numbers in the classical LLL algorithm can reach O(n·β) in the worst case, with an overall complexity of O(n⁵·β³) or even higher.67% similar
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