MATHEMATICA demonstration in class on 2/9---without comments

FactorInteger[2700]

{{2, 2}, {3, 3}, {5, 2}}

test = FactorInteger[2700]

{{2, 2}, {3, 3}, {5, 2}}

test

{{2, 2}, {3, 3}, {5, 2}}

Length[test]

3

test[[2, 1]]

3

test[[2]]

{3, 3}

FactorInteger[Pi]

FactorInteger :: facn : Argument π in FactorInteger[π] is not an exact number. More…

FactorInteger[π]

3^4 + 25 * 23

656

6 + 12/4 * 2

12

6 + 12/(4 * 2)

15/2

EulerGamma

EulerGamma

N[EulerGamma]

0.577216

N[EulerGamma, 16]

0.5772156649015329

N[EulerGamma, 2000]

N[EulerGamma]

FactorInteger[100000000022222444444444444444444444444444444444444444447777777444444444444444444444444444444444222000111111111]

{{5651, 1}, {117497, 1}, {1029472899731, 1}, {146296183339591752940985308176184516211525843160328522539394926791286040403899095883557223, 1}}

FactorInteger[100000000022222444444444444444444444444444444444444444447777777444444444444444444444444444444444222000111111344555111111]

$Aborted

Prime[60]

281

Prime[Range[60]]

Range[60]

Range[60, 100]

{60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100}

PrimePi[200]

46

test2 = Table[PrimePi[n] , {n, 1, 200}]

test2 = Table[PrimePi[n] , {n, 1, 200}] ;

ListPlot[test2]

[Graphics:HTMLFiles/MathematicaDemo_49.gif]

-Graphics -

Plot[PrimePi[x], {x, 1, 20000}]

[Graphics:HTMLFiles/MathematicaDemo_52.gif]

-Graphics -

Plot[{PrimePi[x], x/Log[x]}, {x, 1, 20000}]

[Graphics:HTMLFiles/MathematicaDemo_55.gif]

-Graphics -

Some additional useful MATHEMATICA commands
not demonstrated in class on 2/9

Prime[46]

PrimeQ[11]

PrimeQ[111]

PrimeQ[1111]

FactorInteger[1111]

Plot[PrimePi[x], {x, 2, 100}]

Plot[{PrimePi[x], Log[2, x]/2, x/Log[x]}, {x, 2, 100}, PlotStyle→ {GrayLevel[.1], Hue[0], GrayLevel[.6]}, Background→RGBColor[1, 1, .6]] ;

Plot[{PrimePi[x], Log[2, x]/2, x/Log[x]}, {x, 2 * 10^6, 10^7}, PlotStyle→ {GrayLevel[.1], Hue[0], GrayLevel[.6]}, Background→RGBColor[1, 1, .6]] ;

HarmonicNumber[1000]

N[HarmonicNumber[1000]]

N[HarmonicNumber[5 * 10^5]]

N[HarmonicNumber[10^(50)]]

Denominator[HarmonicNumber[100]]

FactorInteger[%]

Length[%]

ListPlot[Table[HarmonicNumber[n] - Log[n] - 1/(2n), {n, 1, 50}]]

[Graphics:HTMLFiles/MathematicaDemo_73.gif]

-Graphics -

N[EulerGamma, 10]

0.5772156649

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