An algorithm and estimates for the Erdős–Selfridge function
Document Type
Article
Publication Date
December 2020
Publication Title
Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), Open Book Series
First Page
371
Last Page
385
DOI
https://doi.org/10.2140/obs.2020.4.371
Abstract
Let p(n) denote the smallest prime divisor of the integer n. Define the function g(k) to be the smallest integer >k+1 such that p((g(k)k))>k. We present a new algorithm to compute the value of g(k), and use it to both verify previous work and compute new values of g(k), with our current limit beingg(375)=12863999653788432184381680413559.We prove that our algorithm runs in time sublinear in g(k), and under the assumption of a reasonable heuristic, its running time isg(k)exp[−c(kloglogk)/(logk)2(1+o(1))] for c>0.
Recommended Citation
Sorenson, Brianna; Sorenson, Jonathan; and Webster, Jonathan, "An algorithm and estimates for the Erdős–Selfridge function" Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), Open Book Series 4/1 (2020): 371-385.
Available at https://digitalcommons.butler.edu/facsch_papers/1341
