(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 4.2'

                    Mathematica-Compatible Notebook

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Notebook[{

Cell[CellGroupData[{
Cell["Demo Priemtesten", "Title"],

Cell[CellGroupData[{

Cell["Het commando PowerMod", "Subsection"],

Cell["\<\
Hier is een voorbeeld van een pseudo-priemtest met behulp van \
Fermat\
\>", "Text"],

Cell[BoxData[
    \(n = \((10^71 - 1)\)/9\)], "Input"],

Cell[BoxData[
    \(PowerMod[2, n - 1, n]\)], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["Het commando FactorInteger", "Subsection"],

Cell["\<\
Voor getallen met 60 of meer cijfers lukt de ontbinding nauwelijks \
meer. Hier is een voorbeeld\
\>", "Text"],

Cell[BoxData[
    \(n = \((10^67 - 1)\)/9\)], "Input"],

Cell[BoxData[
    \(FactorInteger[n]\)], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["Het commando PrimeQ", "Subsection"],

Cell[TextData[{
  "Het commando ",
  StyleBox["PrimeQ",
    FontWeight->"Bold"],
  " voert een Rabin pseudo priemtest uit. Indien dit commando ",
  StyleBox["False",
    FontFamily->"Courier"],
  " als uitkomst geeft, dan is dit 100 procent betrouwbaar, de uitkomst ",
  StyleBox["True ",
    FontFamily->"Courier"],
  "is 99,9999999... procent betrouwbaar. Volgens de ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " documentatie is er nog geen enkel samengesteld getal bekend waarvoor ",
  StyleBox["PrimeQ",
    FontWeight->"Bold"],
  " het antwoord ",
  StyleBox["True",
    FontFamily->"Courier"],
  " oplevert.\n\nOndanks de ongeschiktheid als echte priemtest is ",
  StyleBox["PrimeQ",
    FontWeight->"Bold"],
  " wel geschikt om kandidaat priemgetallen te ontdekken. Bijvoorbeeld om \
kandidaatpriemgetallen in een interval te localiseren."
}], "Text"],

Cell[BoxData[
    \(For[k = 10^100, k < 10^100 + 1000, \(k++\), 
      If[PrimeQ[k], Print[k]]]\)], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["De Lehmer priemtest", "Subsection"],

Cell["\<\
We proberen een priemgetal van de vorm 7.2^k+1 met k>400 te vinden.\
\
\>", "Text"],

Cell[BoxData[
    \(For[k = 400, k < 800, \(k++\), nn = 7*2^k + 1; 
      If[PowerMod[2, nn - 1, nn] == 1, Print[k]]]\)], "Input"],

Cell["Nu testen of 7.2^432+1 werkelijk priem is.", "Text"],

Cell[BoxData[
    \(nn = 7*2^432 + 1\)], "Input"],

Cell[BoxData[{
    \(\(a = 2;\)\), "\[IndentingNewLine]", 
    \(PowerMod[a, \((nn - 1)\)/2, nn]\), "\[IndentingNewLine]", 
    \(PowerMod[a, \((nn - 1)\)/7, nn]\)}], "Input"]
}, Closed]]
}, Open  ]]
},
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WindowSize->{520, 600},
WindowMargins->{{Automatic, 249}, {Automatic, 63}}
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

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Cell[1880, 59, 94, 3, 32, "Text"],
Cell[1977, 64, 54, 1, 27, "Input"],
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}, Closed]],

Cell[CellGroupData[{
Cell[2125, 73, 48, 0, 29, "Subsection"],
Cell[2176, 75, 120, 3, 50, "Text"],
Cell[2299, 80, 54, 1, 27, "Input"],
Cell[2356, 83, 49, 1, 27, "Input"]
}, Closed]],

Cell[CellGroupData[{
Cell[2442, 89, 41, 0, 29, "Subsection"],
Cell[2486, 91, 871, 24, 158, "Text"],
Cell[3360, 117, 108, 2, 43, "Input"]
}, Closed]],

Cell[CellGroupData[{
Cell[3505, 124, 41, 0, 29, "Subsection"],
Cell[3549, 126, 93, 3, 32, "Text"],
Cell[3645, 131, 130, 2, 43, "Input"],
Cell[3778, 135, 58, 0, 32, "Text"],
Cell[3839, 137, 49, 1, 27, "Input"],
Cell[3891, 140, 175, 3, 59, "Input"]
}, Closed]]
}, Open  ]]
}
]
*)



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End of Mathematica Notebook file.
*******************************************************************)