Does this have practical implications, as in, is this an algorithm that you'd run in practice, or is it mainly a theoretical bound due to constants hidden in the landau symbol?
The General Number Field Sieve[1], referenced in the paper, is believed to have a better asymptotic runtime performance (and has a number of efficient implementations), but it's runtime is not proven. ECM [2](also referenced in the paper) has better proven, but probabilistic, performance.
So most likely, no. This is primarily of theoretical importance (it is now the fastest, deterministic algorithm with a proven bound), but is not immediately a performance gain on existing algorithms.
So most likely, no. This is primarily of theoretical importance (it is now the fastest, deterministic algorithm with a proven bound), but is not immediately a performance gain on existing algorithms.
[1] https://en.wikipedia.org/wiki/General_number_field_sieve
[2] https://en.wikipedia.org/wiki/Lenstra_elliptic-curve_factori...