Possibly the OP might allow Lehmer's "bicycle chain sieves" <https://en.wikipedia.org/wiki/Lehmer_sieve>, which for several decades were the state of the art in factoring large numbers; according to <http://ed-thelen.org/comp-hist/Mike-Williams-Lehmer.html> the first was made in 1926 and "it was only some time in the early 1960s when computers were fast enough to match these speeds".