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\section{Introduction} \section*{Introduction}  %  Imagine you are strolling in the city with a friend when a car passes by with the license plate number "7614829". Your friend proposes a wager, claiming that the number is composite and offering 10 : 1 odds in your favor. Knowing that your friend has no exceptional ability in mental arithmetic and that it's highly unlikely they saw this car before, you realize they are just guessing. Your mental arithmetic is also insufficient to test the number for primality, but is sufficient to check that $7614829 \equiv 1 \pmod{3}$ and $\frac{1}{\ln 7614829} \approx 0.06$. Arguing from the prime number theorem and observing that 7614829 is odd and is divisible neither by 3 nor by 5, you conclude that the probability 7614829 is prime is $\frac{1}{\ln 7614829} \times 2 \times \frac{3}{2} \times \frac{5}{4} \approx 22\%$. Convinced that the odds are in your favor you accept the bet\footnote{Alas, $7614829 = 271 \times 28099$.}.