## Math/Stat Club Seminar

## Primes, Polynomials, and

49,598,666,989,151,226,098,104,244,512,918

## Dr. Michael Knapp

### Loyola University Maryland

### February 26, 2014

3:00-4:00

### Room: 133 Cohn Hall

Abstract:
In this seminar, I'll talk about one of my new favorite theorems. If you take any positive integer, there's a natural way to turn it into a polynomial. For example 1,234 corresponds to \( 1x^3+2x^2+3x+4 \). It turns out that if the original number is prime, then the polynomial you get has no factors (with integer coefficients).
I'll discuss this theorem and some extensions, including one involving the number in the title.

Note: The number 49,598,666,989,151,226,098,104,244,512,918 is pronounced

49 nonillion 598 octillion 666 septillion 989 sextillion 151 quintillion 226 quadrillion 98 trillion 104 billion 244 million 512 thousand 918.

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