The number field sieve

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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2019, methodology): “[50] and Pollard [51], to factor general integers, and modified by amongst others Gordon [52] and Schirokauer [53, 54] to compute discrete logarithms in finite fields.”
Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices (2012, methodology): “The fastest known factoring method for general integers is the number field sieve, which has heuristic complexity O(2n (logn)) for n-bit numbers [36].”
THE ARITHMETIC OF NUMBER RINGS (2008, unknown): “The recent advances with respect to 'down to earth' problems as integer factoring [Stevenhagen 2008] and primality testing [Schoof 2008c] rely on 'large' number rings and on Galois extensions of finite rings to achieve their goal.”