Prove by contradiction that there is an infinite number of prime numbers.

The 'by contradiction' tells us we need to assume the opposite to begin with: 1) Let's assume there is a finite number of prime numbers2) Let P be the largest prime number (the last one) 3) if we multiply all the prime numbers up to and including P: 2x3x5x7...xP=q (the multiple of all prime number up to and including P)4) consider q+1 5) Will it be divisible by any prime P or less? no, as q is divisible by those and q+1 is only 1 more.6) So this means that either q+1 is Prime, or it has a prime factor larger than P.7) But P is the largest prime factor - this is a contradiction as there must exist a prime larger than PHence there is an infinite number of prime numbers

CL
Answered by Charlotte L. Maths tutor

16566 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate ((x^2)+1)^2


If x=-2,1,2 and the y intercept is y=-8 for y=ax^3+bx^2+cx+d, what is a, b, c and d


I don't understand why the function "f(x)=x^2 for all real values of x" has no inverse. Isn't sqrt(x) the inverse?


given y=(1+x)^2, find dy/dx


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences