TableOfWilsonQuotientFor0N41 2008-04-09 19:49:58 2008-04-11 20:17:01 Data Structure Wilson quotient % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The following table gives the numerator and denominator of the Wilson quotient for $0 < n < 41$, given in their lowest terms. If the denominator is 1, then $n$ is prime, but if the denominator is the same as $n$, then $n$ is composite and the numerator is simply $(n - 1)! + 1$. \begin{tabular}{|r|r|r|} $n$ & Numerator of $W_n$ & Denom. \\ 1 & 2 & 1 \\ 2 & 1 & 1 \\ 3 & 1 & 1 \\ 4 & 7 & 4 \\ 5 & 5 & 1 \\ 6 & 121 & 6 \\ 7 & 103 & 1 \\ 8 & 5041 & 8 \\ 9 & 40321 & 9 \\ 10 & 362881 & 10 \\ 11 & 329891 & 1 \\ 12 & 39916801 & 12 \\ 13 & 36846277 & 1 \\ 14 & 6227020801 & 14 \\ 15 & 87178291201 & 15 \\ 16 & 1307674368001 & 16 \\ 17 & 1230752346353 & 1 \\ 18 & 355687428096001 & 18 \\ 19 & 336967037143579 & 1 \\ 20 & 121645100408832001 & 20 \\ 21 & 2432902008176640001 & 21 \\ 22 & 51090942171709440001 & 22 \\ 23 & 48869596859895986087 & 1 \\ 24 & 25852016738884976640001 & 24 \\ 25 & 620448401733239439360001 & 25 \\ 26 & 15511210043330985984000001 & 26 \\ 27 & 403291461126605635584000001 & 27 \\ 28 & 10888869450418352160768000001 & 28 \\ 29 & 10513391193507374500051862069 & 1 \\ 30 & 8841761993739701954543616000001 & 30 \\ 31 & 8556543864909388988268015483871 & 1 \\ 32 & 8222838654177922817725562880000001 & 32 \\ 33 & 263130836933693530167218012160000001 & 33 \\ 34 & 8683317618811886495518194401280000001 & 34 \\ 35 & 295232799039604140847618609643520000001 & 35 \\ 36 & 10333147966386144929666651337523200000001 & 36 \\ 37 & 10053873697024357228864849950022572972973 & 1 \\ 38 & 13763753091226345046315979581580902400000001 & 38 \\ 39 & 523022617466601111760007224100074291200000001 & 39 \\ 40 & 20397882081197443358640281739902897356800000001 & 40 \\ \end{tabular}