5.4 notes - -We could multiply all the primes together, add...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
5.4 More on Primes: Fact 4.1 (Primality test) Thus to test whether N is prime one need to check divisibility by the primes. Example is 179 prime. -14 2 =196 -179 is not divisibility by 2,3,5,7,11,13 -Thus 179 is prime. Theorem 4.5 There are infinitely many prime numbers. Proof: The list of all prime numbers is either finite of infinite. We will show that it is logically impossible for it to be finite. If there were finite many primes, we could write them in order: 2,3,5,7,11,….,p where p is the largest prime number.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -We could multiply all the primes together, add a and call the resulting number N: N=(2*3****P)+1. If we divide N by any prime on the list, the remainder is a. Thus N is not a multiple of any prime. But that contradicts the fact that every whole number is a multiple of a prime. This contradiction means that our assumptions that there is a largest prime P is not true. The list of primes never ends. Proof by Contradiction: pg 123...
View Full Document

This note was uploaded on 04/26/2010 for the course MTH 201 taught by Professor Kwon during the Spring '10 term at Michigan State University.

Ask a homework question - tutors are online