561
Christmas break reading included Those Fascinating Numbers by Jean-Marie De Konnick. The plot is simply one to the Skewes number . Many of the concepts are simply beyond me due to my own lack of grounding in number theory. I was, however, introduced to Fermat's Little Theorem and became interested in the Carmichael numbers . The smallest Carmichael number, however, is 561. An attempt, however, to calculate the number 2 560 on a calculator, let alone any other base, caused smoke to come out of my calculator. An error message was all I could achieve. Still desiring to see if indeed 561 divided evenly into ((2^560)-1), I decided to throw the equation at WolframAlpha. I entered ((2^560)-1)/561 and WolframAlpha dutifully returned 6727205748344993497756781784292814422311802531936613954324788413985069808185648577693630526163384612373383912710808992691213163333199273854833216134461133767645980975 and no remainder. Little wonder my calculator failed to get that right. 166 digits. ...