I am wondering why is quadratic sieve better than Pollard's $\rho$ for integer of $10^4-10^{10}$ digits? The running time of quadratic sieve is $e^{(1+o(1))\sqrt{\ln n\ln \ln n}}$, but the Pollard's $\rho$ only has $O(n^{1/4}$. Isn't this much quicker than the running time of quadratic sieve?
2026-04-05 19:37:10.1775417830
Pollard's $\rho$ algorithm and quadratic sieve
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