Difference between revisions of "Euclid's proof of the infinitude of primes"

(Move to Euclid's Theorem)
(Tag: New redirect)
 
(11 intermediate revisions by 6 users not shown)
Line 1: Line 1:
This is proved by contradiction. Suppose there is a finite number of primes and let them be <math>p_1,p_2,p_3,...,p_n</math>. Let <math>x=p_1p_2p_3\cdots p_n</math>. Then we have <math>x+1=p_1p_2p_3\cdots p_n+1</math>. When divided by any of the primes <math>p_1,p_2,p_3,...,p_n</math>, <math>x+1</math> leaves a remainder of 1 implying that either <math>x+1</math> is prime or that it has some other prime factors not in the set <math>\{ p_1,p_2,p_3,...,p_n\}</math>. In any case we have it so that <math>\{ p_1,p_2,p_3,...,p_n\}</math> does not contain all prime numbers. Contradiction!
+
#REDIRECT [[Euclid's Theorem]]

Latest revision as of 17:56, 21 February 2025

Redirect to: