Let $p\in\mathbb N$ be a prime. I want to prove that there is an infinite amount of primes $p$ with the property $p+2$ is not a prime. I am stuck on how to do this, though. I have tried an alternation of Euclids proof of the infinitude of primes but I cannot seem to find a construction that implies the desired result. Any help would be appreciated.
Asked
Active
Viewed 132 times
3
-
Here is a very similar question. You can apply the same method to your one and observe the steps that they use. – Toby Mak Oct 21 '17 at 09:30
-
Thank you for your suggestion. I have found that page myself before, but the proofs there (stated the way they are) do not fully make sense to me. I was hoping someone could give a different proof or a differently worded proof from those on that page, fitting my specific problem. – Tyron Oct 21 '17 at 10:02
-
The problem on that page is exactly the same as yours. The top two rated answers could hardly be simpler. What doesn't make sense to you about them? – Paul Sinclair Oct 21 '17 at 14:36
-
I don't really know, sometimes I just can't understand a proof if it is formulated in a certain way. Anyway, the page that my answer was a duplicate to contained an answer that made perfect sense to me. Thank you all for your help! – Tyron Oct 21 '17 at 19:31