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"Understanding prime numbers through differentiation and quadratic functions

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Prime numbers been studied since ancient times- this talk will explore prime numbers.

What
  • Connacht
  • Galway
  • Public
When Oct 14, 2009
from 08:00 PM to 09:00 PM
Where Cairnes Theatre, NUI Galway
Contact Name Dr Edwin O'Shea, NUI Galway
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8.00pm Wednesday October 14, Cairnes Theatre, NUI Galway

Public lecture by Dr Edwin O'Shea, NUI Galway

Talk title
"Understanding prime numbers through differentiation and quadratic functions"

Talk description
We will first talk about the fact that there are infinitely many prime
numbers. This was first proved 2,500 years ago and one of the most beautiful
proofs of this claim is based on knowing the derivative of the natural log
function, f(x) = ln(x). Amazingly, this proof tells us that there are at
least ln(x) many prime numbers between 1 and x.
Next we will talk about quadratic functions: the polynomial n^2 - 79n + 1601
produces primes when we replace n with 0 or 1 or 2 or 3. Will this work for
every integer that we replace n with? Come to find out!

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