Article
An algorithm and estimates for the Erdős–Selfridge function
Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), Open Book Series
(2020)
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 being
g(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 is
g(k)exp[−c(kloglogk)/(logk)2(1+o(1))] for c>0.
Keywords
- Erdos–Selfridge function,
- elementary number theory,
- analytic number theory,
- binomial coefficients
Disciplines
Publication Date
Winter December 29, 2020
DOI
https://doi.org/10.2140/obs.2020.4.371
Citation Information
Brianna Sorenson, Jonathan P Sorenson and Jonathan Webster. "An algorithm and estimates for the Erdős–Selfridge function" Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), Open Book Series Vol. 4 Iss. 1 (2020) p. 371 - 385 Available at: http://works.bepress.com/jonathan_sorenson/14/