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Unformatted text preview: s. I t is their difficulty to grasp
that makes primes the basis for our modern information security . Whenev er y ou use a
cash machine or v isit a secure website, it is huge prime numbers that encry pt y our
information and make it ex tremely difficult for any one else to pry it back out of the
Prime numbers also hav e the annoy ing habit of not following any pattern. 3,1 37 is a
prime and the nex t one after that is not until 3,1 63, but then 3,1 67 and 3,1 69 suddenly
appear in quick succession, followed by another gap until 3,1 87. I f y ou find one prime
number, there is no way to tell where the nex t one is without checking all the numbers
as y ou go. One possible way to get a handle on how primes are spaced is to calculate, for
any number, how many primes there are smaller than it. T his is ex actly what Riemann
did in 1 85 9: he found a formula that would calculate how many primes there are below
any giv en threshold. Riemann's formula is based on what are called the "Zeta Function ze...
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This document was uploaded on 01/26/2014.
- Winter '13