17: Difference between revisions
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| [[satisfies property::prime number]] || it is the 7th prime number || 2,3,5,7,11,13,'''17''',19,23,29,31, ... (never stops, [[infinitude of primes]]) | | [[satisfies property::prime number]] || it is the 7th prime number || 2,3,5,7,11,13,'''17''',19,23,29,31, ... (never stops, [[infinitude of primes]]) | ||
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| [[satisfies property::Fermat number]], [[satisfies property::Fermat prime]] || <math>F_2</math>, where <math>F_n = 2^{2^n} + 1</math>, starts <math>n = 0</math> || 3,5,17,257,65537 | | [[satisfies property::Fermat number]], [[satisfies property::Fermat prime]] || <math>F_2</math>, where <math>F_n = 2^{2^n} + 1</math>, starts <math>n = 0</math> || 3,5,'''17''',257,65537 | ||
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Revision as of 04:35, 2 January 2012
Summary
Properties satisfied and families it is a member of
| Property or family | Parameter values (if applicable) | First few natural numbers satisfying the property |
|---|---|---|
| prime number | it is the 7th prime number | 2,3,5,7,11,13,17,19,23,29,31, ... (never stops, infinitude of primes) |
| Fermat number, Fermat prime | , where , starts | 3,5,17,257,65537 |
Structure of integers mod 17
Discrete logarithm
Template:Fermat prime discrete log facts to check against
We can take 3 to be a primitive root mod 17, i.e., a generator for the multiplicative group of integers mod 17. With this, the discrete logarithm table from the multiplicative group mod 17 to the additive group mod 16 looks as follows:
Fill this in later