17

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	$F_2$, where $F_n=2^{2^n}+1$, starts $n=0$	3,5,17,257,65537

Structure of integers mod 17

Discrete logarithm

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:

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