I have a question about a proof of "prime numbers are infinite".Its proof by contradiction and It says- assume we have a list of the product of all the primes, we add one to that list and call it n then n = (p_1*P_2*..*P_k) + 1 for some integer k. since n is a natural number it has a dividor q that is prime, since q is prime q1. since q devides n and q devides "the list" then it will devide n - "the list" and since the difference is 1 q =1. this is where I get lost..how can we say that q =1 because it devides 1?

Question

I have a question about a proof of "prime numbers are infinite".Its proof by contradiction and It says- assume we have a list of the product of all the primes, we add one to that list and call it n then n = (p_1*P_2*..*P_k) + 1 for some integer k. since n is a natural number it has a dividor q that is prime, since q is prime q>1. since q devides n and q devides "the list" then it will devide n - "the list" and since the difference is 1 q =1. this is where I get lost..how can we say that q =1 because it devides 1?

zzr0ck3r · Answer

ok I think my book is just strange for saying it = 1 and it is impossible to divide 1 by a prime is the contradiction to the consequent