View Single Post 2019-04-15, 14:55   #26
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

26×7×13 Posts Quote:
 Originally Posted by MathDoggy I will try to fix the proof once again Assume that there exist a finite amount of twin prime numbers. Then we can construct a list, which in this case will be S, S= A1,A2,A3,A4...An Let P be the product of all twin prime numbers in S, P= A1*A2*A3*A4..An Let Q=P+1 If Q is a twin prime number then S is not complete If Q is composite then some prime factor p divides Q, if this factor p were in our list S then it would divide P, but p divides P+1=Q. If p divides P and Q then p would have to divide the difference of the two numbers which, which is (P+1)-P or just 1. Since no twin prime number divides 1, p can not be on the list. This means that at least one twin prime number exists beyond those in the list.
Q is divisible by two. See my previous post.

Also, p doesn't have to be a twin prime, it can be some other prime, like 2 for example.   