Carmichael 3 strong pseudoprimes: Difference between revisions
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The objective is to find Carmichael numbers of the form Prime1 X Prime2 X Prime3. |
The objective is to find Carmichael numbers of the form Prime1 X Prime2 X Prime3. |
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Prime1 < Prime2 < Prime3 for all Prime1 upto 61 see page 7 of [http://www.maths.lancs.ac.uk/~jameson/carfind.pdf Notes by G.J.O Jameson March 2010]. |
:Prime1 < Prime2 < Prime3 for all Prime1 upto 61 see page 7 of [http://www.maths.lancs.ac.uk/~jameson/carfind.pdf Notes by G.J.O Jameson March 2010]. |
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For a given Prime1 |
For a given Prime1 |
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for 1 < h3 < Prime1 |
for 1 < h3 < Prime1 |
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:for 0 < d < h3+Prime1 |
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::if (h3+Prime1)*(Prime1-1) mod d == 0 and -Prime1 squared mod h3 == d mod h3 |
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::then |
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:::Prime2 = 1 + ((Prime1-1) * g/d) |
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:::next d if Prime2 is not prime |
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:::Prime3 = 1 + (Prime1*Prime2/h3) |
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:::next d if Prime3 is not prime |
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:::next d if (Prime2*Prime3) mod (Prime1-1) not equal 1 |
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:::Prime1 * Prime2 * Prime3 is a Carmichael Number |
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=={{header|Ruby}}== |
=={{header|Ruby}}== |
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