Classical Methods of Factorization
The art of factoring large integers was not very advanced before the days of the modern computer. Even if there existed some rather advanced algorithms for factorization, invented by some of the most outstanding mathematicians of all times, the amount of computational labor involved discouraged most people from applying those methods to sizable problems. So the field essentially belonged to a few enthusiasts, who however achieved quite impressive results, taking into account the modest means for calculations which they possessed. Famous among these results is F. N. Cole’s factorization in 1903 of 267 − 1 = 193707721 ∙ 761838257287.
KeywordsPrime Factor Quadratic Residue Search Limit Large Prime Factor Algebraic Factor
- 2′.L. G. Sathe, “On a Problem of Hardy on the Distribution of Integers Having a Given Numbers of Prime Factors, I”, Journ. Indian Math. Soc. 17 (1953) pp. 62–82.Google Scholar
- 7.Karl Dickman, “On the Frequency of Numbers Containing Prime Factors of a Certain Relative Magnitude” Ark. Mat. Astr. Fys. 22A #10 (1930) pp. 1–14.Google Scholar