BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Brianna Sorenson (Butler University)\, Jonathan Sorenson (Butler U
 niversity)\, and Jonathan Webster (Butler University)
DTSTART:20200701T190000Z
DTEND:20200701T193000Z
DTSTAMP:20260423T200345Z
UID:ANTS14/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/13/">
 An algorithm and estimates for the Erdős-Selfridge function</a>\nby Brian
 na Sorenson (Butler University)\, Jonathan Sorenson (Butler University)\, 
 and Jonathan Webster (Butler University) as part of Algorithmic Number The
 ory Symposium (ANTS XIV)\n\n\nAbstract\nLet $p(n)$ denote the smallest pri
 me divisor of the integer $n$. Define the function $g(k)$ to be the smalle
 st integer $ >k+1$ such that $p(\\binom{g(k)}{k}) >k$. We present a new al
 gorithm to compute the value of $g(k)$\, and use it to both verify previou
 s work and compute new values of $g(k)$\, with our current limit being\n\\
 [\ng(360) = 4\\ 73246\\ 49994\\ 16835\\ 77114\\ 34474\\ 66861.\n\\]\n\nWe 
 prove that our algorithm runs in time sublinear in $g(k)$\, and under the 
 assumption of a reasonable heuristic\, its running time is\n\\[\ng(k) \\ex
 p[ -c (k\\log\\log k) /(\\log k)^2 (1+o(1))] \\text{ for } c >0.\n\\]\n\nC
 hairs: Alina Ostafe and Kate Stange\n
LOCATION:https://researchseminars.org/talk/ANTS14/13/
END:VEVENT
END:VCALENDAR